Quantum Communication Networks for Energy Applications: Review and Perspective

The energy sector is expected to undergo significant changes in the coming decades with the advent of new technologies, including smart grid development, microgrid expansion, increasing electric vehicle and renewable energy usage, and enhanced measures to minimize greenhouse gas emission, among others. In tandem, these changes are expected to create new opportunities for the deployment of quantum technologies within the energy sector. Building on the authors' previous reviews on the current state of and future opportunities for quantum sensing, quantum computing and quantum simulations for energy sector applications, this work provides an overview of recent progress in quantum networking and communications for the energy industry, with a focus on platforms, devices, and protocols, including quantum teleportation and quantum key distribution. Specific areas of relevance to the energy sector are then analyzed, including the role of quantum networks for greenhouse gas monitoring, secure data collection and transmission in smart grids, nuclear power plants’ safety, facilitating oil and gas exploration, and other energy‐relevant applications. This review concludes with a brief overview of areas for future innovation, including the need for platforms for simulating quantum networks, quantum material and platform design, and computational approaches to accelerate quantum protocol discovery and development.


Introduction 1.Basics of Quantum Information Science
Quantum information science (QIS) is foundationally based upon principles of quantum mechanics and combines aspects of a range of academic fields, including engineering and the physical sciences, as well as mathematics and computer science. [1]1b,2] Information theory, a second central component to QIS, focuses on the collection, storage, and dissemination of data, and is essential for the performance of modern electronics. [3]Rapid innovations in both quantum mechanics and information science have, in turn, spurred significant growth in QIS over the past 30 years, capturing the imagination of scientists and policymakers alike globally because of the potential breakthroughs QIS may engender.
QIS is typically broken down into four pillars: quantum sensing, quantum networking, quantum computing, and quantum simulations.Early commercial applications have been realized in both quantum simulations and computation, while quantum sensing [4] and quantum networking [1b,5] are also poised to have transformative impacts in the near future.The energy sector is one critical area where the early applications of QIS are expected to have a particularly significant impact. [6]In our previous reviews, [7] we summarized the current status and future outlook of quantum sensing, quantum computing, and quantum simulations for energy applications.Here, we summarize the current state of quantum communications and networking methods and platforms and specifically discuss their existing and potential applications in the energy sector.

Quantum Communications and Networking
Quantum mechanical principles are expected to enable communications and networking with immense network capacity and unconditional security. [8]Quantum communication describes quantum key distribution (QKD, described in Section 2.4) among multiple users for the secure transfer of classical information and quantum teleportation of quantum states from one location to another.The expansion of quantum communication to link multiple users and locations, in turn, requires the development of quantum networks, [9] which consist of multiple quantum nodes.These nodes are usually transmitters, receivers, or repeaters for processing quantum information.Quantum networks are based on the principles of quantum mechanics, such as the superposition principle, the no-cloning theorem, entanglement of manyparticle states, and indistinguishability of non-orthogonal quantum states, which are not available to classical networks.Quantum networks use the quantum properties of photons' quantum states to encode information; these states interact with each other, regardless of their separation distance, which provides the possibility for "spooky action at a distance," a term Einstein used to describe the entanglement of quantum states.Quantum network repeaters that use entanglement to extend the range of quantum networks are being developed, which is a key aspect for practical deployment and commercialization.Quantum communication protocols to formalize these associations need to be developed to allow the quantum state of photons to carry information from the sender to a receiver through a quantum network, and this remains an important research focus.
Numerous devices can form a quantum network capable of transmitting encrypted information using the laws of quantum mechanics, featuring entanglement-enabled quantum teleportation, and paving the way for a quantum internet, a network of quantum computers.Indeed, sophisticated cybersecurity threats have demanded new safeguards to protect data sent over networks, and data encryption is becoming increasingly important. [10]Quantum networking using QKD methods enables secure data transmission over distant networks, preventing data exposure to unintended recipients. [11]These features, their underlying principles, and their application areas within the energy sector in particular, which rely upon the secure collection and dissemination of massive amounts of data, are discussed in detail in this review.

Overview of Quantum Networking for Energy Applications
Quantum networking and communication technologies such as QKD (Section 2.4) have matured significantly over the past several decades, as evidenced by the ever-increasing number of commercial players in the field (Section 2.4.4).Initial applications have been largely geared toward enhanced security for industries such as banking, [12] communication, [13] election systems, [14] and the military, [15] among others.
As quantum networking and communications technologies mature, numerous potential application areas within the energy sector will benefit significantly (Section 3).Notable application areas include:

Global Monitoring of Greenhouse Gases
Greenhouse gas emissions can be monitored and mapped through a sophisticated network of automated sensors, [16] modeling systems, [17] and satellite mapping. [18]Ground-to-satellite quantum communication could significantly enhance the security of the data collected.Moreover, quantum networks of sensors (particularly networks of quantum sensors) will improve the spatial resolution of global mapping, while wireless quantum network development will also facilitate data transmission. [19]

Fossil Energy Infrastructure Monitoring and Automation
Fossil energy infrastructure, such as pipelines, wellbores, and powerplants, rely on sophisticated sensor systems to monitor parameters such as gas emissions, corrosion, and temperature.Automation within natural gas infrastructure relies on communication between sensor networks and system controls.Security protocols such as QKD will be vital for protecting systems from outside attacks that could cause disruption.Moreover, as shown in our previous review, [7] networks of quantum sensors will be increasingly deployed within fossil energy infrastructure and this is expected to produce unprecedented measurement sensitivity.

Oil, Gas, and Electricity Infrastructure Build-Out and Planning
Meeting ever-increasing energy demands will require the continued expansion of fossil energy infrastructure.Satellite-to-ground and underwater quantum networks will improve the sensitivity and security of navigational equipment for subsea oil and gas exploration.Mobile quantum networks such as drones will enable secure monitoring of powerplant emissions and mapping of abandoned infrastructure in remote areas.Notably, quantum security protocols such as QKD will be vital for ensuring the smooth operation of emerging energy infrastructure such as electric vehicle charging stations, microgrids, and driverless vehicle networks, offering quantum-secured protection against cyberattacks and hackers.

Electrical Grid Modernization and Optimization of Interdependent Infrastructure
The expansion of "smart grids," which optimize energy distribution based on consumer usage data, will improve energy efficiency and minimize waste.To accomplish this, smart grids must collect and transmit massive amounts of user data for operation.Similarly, research is ongoing to optimize the performance of interdependent energy networks (for example, transportation, fuel, and power station networks all impact one another) to prevent disruptions, minimize costs, and ensure secure operation.In both cases, quantum security protocols will be essential to protect smart grids and interdependent networks from disruptions due to cyberattacks, viruses, malware, and other security breaches.

Nuclear and Renewable Energy Sectors
Renewable energy technologies such as wind and solar power are highly dependent upon weather events (e.g., the amount of sunlight in a day, the strength and direction of the wind, etc.).Planning sites for renewable energy deployment and predicting the amount of energy produced from these technologies both benefit significantly from accurate weather forecasting.Accurate forecasting data must be transmitted securely between forecasters and energy users for optimal power management, and QKD can ensure secure data transmission.Similarly, QKD is critical for secure communication between networked diagnostic sensors within the nuclear power plant and plant operators, preventing data from being monitored and/or manipulated by third parties.
Continued maturation of quantum networking and communications technologies can therefore have broad impacts in ensuring secure transmission of information during all stages of energy production, transportation, distribution, and consumption, from fossil energy sources to renewables.This review will expand upon these potential application areas while providing an overview of current quantum networking/communication techniques, technologies, and protocols, along with an outlook on future needs and areas for innovation in the field, specifically geared toward energy sector applications.

Scope of the Review
QIS has increasingly become a research priority around the globe, as evidenced by, for instance, the 2018 U.S. National Quantum Initiative Act, which mandated the National Institute of Standards and Technology (NIST), the National Science Foundation (NSF), and the Department of Energy (DOE) to form partnerships with industry and academia to accelerate the development of QIS technologies. [20]This strategy has been mirrored globally, [21] with nations such as the European Union countries, [22] United Kingdom, Canada, [23] Japan, [24] Australia, [25] China, [26] Russia, [27] South Africa, [28] and others also establishing significant funding for QIS-related research.The promise of quantum technologies, from highly sensitive sensors to powerful computers and highly secure information transmission, has driven significant global investments in this area.
Quantum networking and communication is arguably the most mature pillar of QIS, with multiple QKD technology companies currently in the market.Quantum networking and communication are already breaking new ground in cybersecurity applications and promise to benefit from a rapidly evolving global energy sector that is becoming increasingly reliant upon secure information collection and transmission.The scope and outline of the review are illustrated in Figure 1.We first discuss the current state of quantum networking and communication technologies (Section 2), describing devices and platforms used for quantum communication (Section 2.2), the basics of and current innovations in quantum teleportation (Section 2.3), the fundamentals and commercialization of QKD (Section 2.4), quantum transduction (Section 2.5), and microwave quantum communication platforms and protocols (Section 2.6).After describing the current state-of-the-art in quantum networking, we analyze specific energy-sector applications that currently employ quantum networking/communication and areas of need that could benefit from quantum networking/communication (Section 3).This review concludes with an overview of future opportunities and innovation requirements for quantum network deployment within the energy sector (Section 4).Taken together, this review provides both a fundamental overview of the current state-of-the-art in the field of quantum networking and communication and emphasizes the application areas and considerations that are specific to the energy sector.

Progress on Quantum Communications and Networking
The field of quantum communication and networking has grown rapidly over the last three decades.In a broad sense, quantum networking covers areas of communication as implemented on different platforms, such as silicon-based materials or nonlinear optical dielectric materials capable of executing systems such as QKD and quantum teleportation based upon quantum-enhanced protocols.QKD can be integrated within hybrid classical-quantum platforms and is feasible via manipulating qubits in the path of photons using nonclassical resources (Section 2.4). [29]By contrast, quantum teleportation (Section 2.3) is a protocol in quantum information that exploits entanglement and allows for quantum state transfer. [30] significant attempt has been made to develop networking technologies enhanced by quantum laws.To understand researchers' efforts over the past 30 years, we summarize the number of publications in quantum networking, quantum communication, QKD, and quantum teleportation in Figure 2.This figure illustrates that the total number of research and development contributions has generally rapidly increased since 2000, following a spike in research activity from 1995-1998.
It is evident from the rapid growth in the number of quantum networking-related publications that research institutions around the globe are pursuing quantum networking and communication as a major part of their research strategies.Here we provide a detailed review of both the fundamentals and recent innovations related to quantum communication, teleportation, and QKD.

Quantum Communication Platforms and Devices
The possibility of connecting individual quantum systems using channels and establishing secure communication is envisioned to enhance existing classical networking systems. [31]11a,32]

Integrated Quantum Communication Platforms
The platforms for quantum communication are expected to meet not only specific requirements for quantum state generations, manipulations, storage, and detection but also criteria pertaining to mass production, cost-effectiveness, and scalability.The development of integrated quantum photonic platforms for chip-based quantum communication applications is therefore a key research thrust for economical and scalable production. [33]Major potential platforms [34] include i) silicon-based materials such as silicon nitride (SiN) [35] and silicon carbide (SiC), [36] ii) III-V semiconductors such as indium phosphide (InP), gallium nitride (GaN), [35] and gallium arsenide (GaAs), [37] iii) nonlinear optical materials such lithium niobite (LiNbO 3 ), [38] and iv) nitrogen-vacancy (NV) centers in diamond. [39]Silicon-based technologies are wellestablished and can also be used to achieve quantum features. [40]Copyright 2016, The Optical Society (OSA).Silicon chips built with fiber interconnects between chip A and chip B (b, c) and spiraled sources of photon pairs, and path and polarization encoding qubit converters (d, e, f).Reproduced under terms of the Creative Commons (CC BY) Attribution 3.0 license. [43]Copyright 2014, American Physical Society.
Photonic graph states are building blocks for scalable quantum technologies.Photonic generators of arbitrary graph states in a miniature silicon chip can encode quantum information in more than one pair of photons generated on the chip, as shown in Figure 3a. [42]Silicon devices are also built with fiber interconnects between two chips and spiraled sources of photon pairs with polarization encoding qubit converters, as shown in Figure 3d-f. [43]Similarly, III-V compounds provide opportunities for tuning the material's band gap over a wide range and can produce required quantum features such as parametric downconversion via manipulation of light.These materials have strong second-order nonlinearity, which, along with the electro-optic effect present in the family of niobite materials, makes them ideal candidates for quantum communication platforms.
III-V compounds are well-studied and are expected to be relevant for quantum-enhanced technological development. [44]Indeed, semiconductor quantum dots are attractive due to their high brightness, optical efficiency, and purity, and this material class has been widely used in an ext range of quantum devices. [45]41c,44] NV color centers in diamond preserve their quantum character up to room tempera-ture, an important consideration for practical deployment.NV centers provide a platform for transferring quantum information into a quantum memory without revealing or destroying the stored information. [46]However, major fabrication challenges make diamond a difficult platform to work with when creating integrated optical photonic circuitry.Other alternatives such as SiC are being actively pursued, however they also have their own challenges, particularly when searching for adequate analogs of NV center-like color centers possessing good coherence and optical properties. [47]In addition, when scaled-up, on-demand fabrication remains a barrier. [48]LiNbO 3 is also currently limited by fabrication issues, including the small size of commercially available wafers and high cost-per-wafer, among other challenges. [47,49]

Quantum Communication Devices
Quantum communication devices generate, manipulate, store, and detect the quantum states of photons.The propagation of signals at telecommunication wavelengths through optical fibers and at infrared wavelengths through atmosphericallytransparent windows minimize loss.Certain systems like QKD protocols require a single photon quantum state.A single  [55a] Black-red and blue-red color bars correspond, respectively, to intensity and intensity correlation measurements.55a] Copyright 2019, American Physical Society.A schematic of a SOI chip-scale device consisting of four telecommunications-band photon-pair sources, which produce four photons in superposition (e).A qubit demultiplexer for configuring the superposition into a product of two Bell-pair, a reconfigurable post selected entangling gate (R-PEG) and four single-qubit projection and analysis stages (a Mach-Zehnder type interferometer).Reproduced under the terms of the Creative Commons (CC BY) license. [56]Copyright 2019, Springer Nature.quantum state can be produced probabilistically by heralding the desired state from one of the two photons in an entangled photon pair or deterministically by using a single photon emitter.Sources that generate correlated photon pairs are used to produce heralded single-photon states used in quantum communication and to create two-photon entangled states called Einstein-Podolsky Rosen (EPR) pairs.Entangled photon pairs are mainly generated in two ways: by using spontaneous four-wave-mixing (SFWM) or by utilizing spontaneous parametric down conversion (SPDC), which is also known as parametric fluorescence. [50]50b,51] Possibilities for generating polarization-entangled states with more than 90% fidelity have been demonstrated by using a very tight bending radius and strong mode confinement in SOI-based waveguides. [52]ntangled photon pairs have also been generated in -barium borate (BBO) crystals with 96% fidelity when pumped with an elliptical spatial profile. [53]SPDC is another popular technique for producing spatially entangled photon pairs, where a coherent Gaussian beam of light illuminates nonlinear crystals that produce a pair of photons. [54]This technique has been used to generate spatially entangled photons with a specific degree of entanglement by controlling the spatial coherence of the pump beam with rotating random diffusers, as shown in Figure 4. [55] Photonic graph states are another promising quantummechanical method for describing the states of entangled photons.Graph states can be drawn as a graph with a qubit on each vertex and pair-wise entanglement on each edge. [57]easurement-based protocols using graph states integrated into silicon photonics offer opportunities for scaling up optical functionality.Such platforms also play a central role in simulating complex processes and dynamics in quantum mechanics. [58]raph states are extensively studied in optics-related experiments and other platforms. [59]Recently, photonic graph states have been produced and encoded on a mass-manufactured chip using four on-chip generated photons (Figure 4e). [56]This platform essentially integrates existing silicon technology with the entanglement features in the on-chip multipair photon sources and will be useful for future scalable quantum information processing.The fabrication of nanocavity arrays with high Q factors are another important technology for the development of integrated quantum devices, as coupling between cavities can be exploited for Figure 5. a) A schematic for a basic quantum teleportation protocol where Alice's unknown input state a is teleported to Bob using a shared entangled state.Alice uses classical communication to pass the outcomes of the measurement to Bob.Reprinted with permission from Ref. [30].Copyright©2015, Springer Nature.b) A schematic for a quantum communication network expanded over long distances.Each node has a quantum memory of an atomic cloud that consists of write-and read-out protocols.Reproduced with permission. [32]Copyright 2012, National Academy of Science.
41b,c,60] Moreover, the integration of cavity networks with fiber optics is also an intriguing platform for long-distance quantum communication. [60]These devices would enable the production of low-loss and long-distance fiber-optic quantum links for secure communications.Continued optimization of these platform components is crucial for the development of scalable, high-performance quantum communication devices.

Quantum Teleportation
Quantum teleportation is a protocol in quantum information theory that exploits quantum entanglement. [61]It plays a fundamental role in developing the basic theory for quantum information and quantum technologies. [62]The term "teleportation" was first coined in 1931 by Charles H. Fort, [30] and has been understood as a process by which objects are transferred from one location to another without actually making the journey connecting these two locations. [63]69a,72] Long-distance ground-and satellite-based teleportation has also been successfully achieved in several experimental observations. [30,73]Here, we review the basics of quantum teleportation and its variants and briefly discuss its current experimental status.

Quantum Teleportation Basics
Quantum teleportation with discrete variables (DVs) is based on natural photodetection and consists of built-in entanglement distillation after losses. [74]A simple concept of DV quantum tele-portation schemes can be understood from a well-known example of Alice and Bob, which was first used to describe twolevel quantum systems as shown in Figure 5a. [30,63]This is a basic protocol in which Alice and Bob share two qubits (A and B) prepared in an entangled state, also known as a Bell pair: Alice is given another input qubit a with unknown state .She performs a Bell detection, [63] which projects a and A into one of the four Bell states, which are leveled by k = 0, 1, 2, 3.As a result of the measurement, Alice's input is collapsed.She communicates the classical outcome k to Bob. Bob applies the conditional unitary U k to his system B, retrieves an output that is an exact copy of qubit a, the input Alice is given (for 100% fidelity).Such a scheme can be expanded to multiple nodes covering a long distance where each node carries basic elements such as quantum memory for storing, writing, and reading out the states during the teleportation (Figure 5b).
Teleportation is not limited to qubits; it can also involve higher dimensions in the Hilbert space.A maximally entangled state and unitary basis of dimension d satisfying the relation U + i , U j = d ij are used to generate vectors that are also maximally entangled. [75]Using a DV system, one can construct such protocols for finite-dimensional Hilbert space.
Quantum teleportation spanning the infinite-dimensional Hilbert space is known as a continuous variable (CV) system. [76]he CV system takes advantage of the semi-classical approach for deterministic state preparation and is relatively simpler than the DV system because it can be integrated within existing technologies.Such protocols can be realized using bosonic optical modes where position-momentum quadrature operators describe the electric field.69e,70a] Quantum teleportation has enabled breakthrough schemes in linear optical quantum computing, such as Figure 6.Illustration of the idea of quantum repeaters (left panel).A long-distance quantum entanglement between A and Z is achieved through multiple steps: a) Elementary entanglement between the locations A, B, C……X, Y and Z are established, entanglement is swapped with the neighboring links, and the process is repeated over and over in hierarchical fashion until the entanglement is distributed over the desired location.Yellow squares represent the quantum memory (QM).The dotted arrows connecting two remote memories indicate they are entangled. [91]A model of optically controlled quantum memory using a quantum dot (right panel).Polarization of e-h pairs are used to define qubits in a quantum dot.(a) Write-out can be done by exciting an electron (dark spheres) using a pump pulse.(b) Information stored in the excited e-h pairs can be read out using a detuned probe pulse.86a]  and m j are the angular and spin quantum numbers in the quantum dot.Left panel: Reproduced with permission. [91]Copyright 2011, American Physical Society.86a] Copyright 2013, American Physical Society.
the Knill-Laflamme-Milburn (KLM) algorithm.For details on the KLM algorithm, we refer the reader to reference. [79]

Entanglement Swapping and Repeaters
Implementing quantum communication protocols requires a quantum channel, repeater, and computer, each dedicated to executing specific tasks.First, a quantum repeater establishes entanglement with each computing node individually by transmitting photons through an optical fiber.In the subsequent step, a repeater teleports the qubit entangled with one node to the other node by a process called entanglement swapping.Long-distance entanglement can be established in this way.11a] Therefore, in full quantum architectures, transmitting information between two remote quantum computing nodes happens through quantum teleportation. [80]This is in contrast to information processing in classical communication architectures where the same particles/photons carrying information about one system are transported to the system at the destination.
The key idea of the quantum repeater approach is to create entanglement over a distance d by swapping two entangled pairs, each of which covers a d∕2 distance. [81]For N = 2 n elementary links, each with a covered distance of d∕N, one can establish entanglement over a distance d with n levels of entanglement swapping operations, as shown in Figure 6.
Despite significant progress, the development of a practical quantum repeater remains a challenge due to limitations in quantum memories.One recent approach relies upon nodes comprised of rare earth ion-doped crystals (Nd 3+ :YVO 4 ) as absorptive quantum memories and a polarization-entangled photon pair source, which may offer advantages for multiplexing over extended distances. [82]Alternatively, an all-photonic quantum repeater has been shown to eliminate the need for quantum memories.These are repeater graph states (RGS) consisting of a complete subgraph for photons.This approach is resilient against diminishing photon counts and avoids limitations due to coherence time and long-distance heralding. [83]ong-distance quantum communication processes such as teleportation may also be aided by entanglement purification protocols (EPPs).Here, localized operations are performed on less entangled states, which are consumed, and a smaller number of maximally entangled states are produced. [84]An EPP protocol was recently demonstrated that improved the fidelity of polarization entanglement from 0.771 to 0.887 (along with other performance figures of merit) at a distance of 11 km, illustrating the potential of EPP for long-range applications. [85]uantum Memory: An essential component of a quantum repeater is quantum memory, which increases the achievable communication distance between two nodes, thus improving the architecture's scalability.Currently, internodal distance is limited by a propagation loss of photons in an optical fiber.Quantum memory based on electron-hole (e-h) pair polarization in quantum dots has been shown to store qubits and entangle photons with a single e-h pair or a single electron or hole. [86]Atomic ensembles such as rare earth-doped crystals reach a sub-second coherence time, with a storage time of milliseconds, [87] and are thus also excellent candidates for possible applications in quantum memory. [88]The NV center is a particularly promising qubit candidate that allows quantum communication over very long distances without data loss.69a] Even though trapped ions have short distance limitations due to the short-range Coulomb interaction, the storage time in such systems is exceptionally long, [89] with storage lifetimes in the tens of seconds range. [90]As such, multiple promising candidate platforms are promising for quantum memory, each with associated advantages and challenges.The choice of quantum memory materials will thus depend on factors such as the required coherence time, distance, coupling strength between light and matter, transmission losses and temperature.
Information encrypted in qubits and transmitted over quantum networks is protected by the no-cloning theorem, which states that copying an unknown quantum state is impossible without destroying it at the origin. [92]Any third-party attempt to steal data that are teleported over the quantum channels would violate the no-cloning theorem; therefore, that action would be impossible.Thus, quantum teleportation protocols (e.g.QKD provide an encryption method that is in principle unbreakable.

Quantum Teleportation Network
The example of Alice and Bob above describes a simple scheme of two-party teleportation.If more than two parties initially share entangled states, a network of quantum teleportation is established, where teleportation occurs between any two parties. [93]In assisted teleportation, a third party, Charlie, can assist in increasing the fidelity of the entanglement between Alice and Bob.For that, first Alice teleports an entangled photon to both Bob and Charlie.Charlie makes a local measurement and broadcasts the result.
In the non-assisted teleportation scheme, Charlie does not help Alice; instead, he also receives a copy using a telecloning protocol.Alice teleports to both Bob and Charlie, but the fidelity is limited by the no-cloning theorem. [94,95]Such a scheme has been experimentally achieved with polarized photonic qubits [96] and coherent states of optical modes. [97] network of short-distance teleportation is promising due to the rapid development of quantum computers, which require gate operations to be performed between qubits separated by increasingly large distances as computers incorporate more qubits.Pfaff et al. [69a] achieved quantum teleportation between two nitrogen vacancies in diamonds that were separated by 3 m (Figure 7), investigating the potential of networked quantum computing.These spins were manipulated and pumped by microwave excitations at the ground level.Spins were entangled via an entanglement swapping method.The nuclear spin state of the nitrogen ion at the first center was prepared and detected together with the state of the electronic spin of the same center and teleported to the state of the electronic spin at the second center with an estimated fidelity of 86%.A promising route of this concept is the use of weakly-coupled nuclear spins with coherence times greater than 1 s under optical excitations. [98]This enables a robust scheme for quantum teleportation using solid-state spins placed in a cavity, which allows for remote entanglement within milliseconds.A fully remote, 3-node quantum network was later developed based upon photon-coupled NV qubits which demonstrated both entanglement distribution and entanglement swapping protocols.Here, node A was separated by nodes B and C by a 30 m optical fiber, while node B, equipped with a 13 C spin quantum memory, was separated from node C by a 2 m optical fiber. [99]n 2019, Wan's group demonstrated quantum gate teleportation by teleporting a controlled NOT gate between spatially separated trapped ions. [100]Such demonstrations highlight the interdependence between innovations in quantum computing and quantum networking.

Long-Distance Quantum Teleportation
Quantum Teleportation Using Fiber Optics: Distributed optical fiber networks provide a promising platform for the entanglement and teleportation of photonic qubits without requiring large-aperture optics.Transmission photon loss within the telecom band below 0.25 dB km −1 has been achieved through fibers. [101]While photon transmission using fibers suffers some loss and requires repeaters for teleportation over relatively longer distances, high-fidelity teleportation can be achieved within intracity distances.
64a,b] In successive experiments, teleportation of states from light to matter [70a] and matter to matter [89b,102] were also achieved.Bao et al. [31b] conducted an experiment with quantum memories composed of atomic ensembles separated by 0.6 m at two ends, each playing the role of Alice or Bob.Each atomic ensemble represented an elementary quantum network node that consisted of 10 8 rubidium atoms and was connected to the other by a 150 m optical fiber.In the experiment, a quantum teleportation protocol was established over the full length of the fiber.A time-bin qubit (i.e., a single photon populating one of two temporal modes) was teleported along a 2 km telecom fiber with 25% Bell-efficiency and 81% fidelity [103] by using two different wavelengths of 1.3 and 1.5 μm (both of which are in the telecom band).In a similar experiment, a Bell measurement was conducted by a third party connected with Alice's input state and the entangled source by means of a 2 km fiber. [104]A polarized photon in the telecom band was teleported to the state in the solid-state quantum memory.Another experiment [38] stored the photon state in a rare earth ion-doped crystal and that photon was polarization-entangled with a flying telecom photon.Quantum teleportation was achieved between the solid-state memory and the telecom photon state over 25 km of combined distance covered by two qubits.The operation of a platform-independent quantum gate has been demonstrated between two independent quantum networks separated by a 60 m optical fiber. [105]uantum entanglement at a distance of 33 km using trapped rubidium ions was demonstrated in 2022. [106]Significantly, Tittel and co-workers executed a quantum teleportation protocol at a distance of 6.2 km using the city of Calgary's telecommunication network, a practical demonstration in a "real-world" urban environment. [107]Collectively, these experiments demonstrate the wide variety of methods and platforms that may be used to achieve long-range quantum teleportation.Significantly, Nakazawa et al. reported the first on-line, high-speed, largecapacity, secure optical communication system using quadrature amplitude modulation (QAM).Up to 70 Gbits s −1 single channel transmission over 100 kilometers was achieved with a spectral efficiency of 10.3 bits Hz −1 , [108] a key step toward establishing a market-ready network.
69a] Copyright 2014, American Association for the Advancement of Science.
Hilbert spaces are used instead of qubits.CV entanglement can be efficiently produced using squeezed light due to nonlinear optical interactions.In this approach, Gaussian entanglement is used between two parties that rely upon the Braustein-Kimble (BK) protocol. [109]The CV approach is more suitable for photonic chip integration than the DV approach when implemented for QKD. [110]For example, a fiber-based CV-QKD system demonstrated a secure key rate of about 1 kbps over an 80 km transmission length. [111]In a separate study, a secret key rate of 0.14 kbps was achieved over a simulated distance of 100 km in fiber using integrated silicon photonic devices. [112]The drawback is that the implementation of quantum teleportation with the CV approach comes at the expense of the quality of the entanglement of prepared states.DV and CV QKD are discussed further in Sections 2.4.2 and 2.4.3, respectively.
One challenge of teleportation using fiber optics is to maintain the indistinguishability of photons after they travel over a long distance before the Bell state measurement is performed.In a study attempting to mitigate this challenge, photons were passed through a long-coiled fiber before they were detected using the Bell state measurement. [104]A crucial point is that the photons are expected to arrive within their coherence time, which is typically less than a picosecond.The authors determined that temperature differences between the two fiber spools can significantly impact the distance travelled due to thermally induced fiber length variations (8 mm/K for a 2 km fiber).Placing both fibers on the same spool helped mitigate these effects.The effect of temperature can also be minimized by extending the coherence time of photon pairs to several hundreds of picoseconds.
The challenge in QKD is that quantum information encoded in the photon polarizations that are transmitted over the optical fiber network suffers unrepairable loss.Unlike classical communications, where large losses can be mitigated through signal regeneration using devices such as Er-doped amplifiers, the quantum no-cloning theorem prohibits loss regeneration in QKD.92a] To circumvent that problem scientists have proposed the use of quantum repeaters [81,113] between the sender and receiver so that information can be repeated at every station and passed to the next station.Quantum repeaters (see Section 2.3.2) combine two basic features, quantum entanglement swapping [59b] and quantum memories, [86a,114] and are expected to repeat the quantum information sent over long distances in terrestrial communications.
Quantum Teleportation Using Satellite: Quantum teleportation using fiber optics or fully atmospheric channels suffers from photon loss that scales exponentially with the channel length.The reduced photon intensity arriving at the detector cannot be amplified due to the non-cloning property of quantum states.One solution to this problem is to use a quantum repeater protocol at certain distance intervals as described above.However, this approach requires long storage and coherence times of qubits, which both present challenges.
The possibility of quantum teleportation through atmospheric channels not only provides an opportunity to connect ground-toground communications but also to connect satellite-to-ground (downlink) or ground-to-satellite (uplink) communications, enabling the integration of satellites in the quantum network. [115]ntegrating satellites in the quantum network has the benefit of achieving low loss of quantum information because the effective thickness of the atmosphere over which the photons must travel is just about 10 kilometers, which means photons travel mostly in free space. [116]here have been several high-profile demonstrations of quantum teleportation using satellites over the past few years.Ren et al. [117] describes quantum teleportation protocols experimentally realized over a length of 1400 kilometers that established satellite communication to a ground station (Figure 8).This experiment illustrates the possibility of building quantum networks connected through channels and transmitting over the atmosphere on a global scale.In a similar experiment, [115e] Yin et al. demonstrated a satellite-based quantum entanglement distribution of photon pairs separated by over 1200 kilometers.The physical distance between the ground stations (located at Delingha and Lijiang, China) and the satellite varied between 500 to 2000 km.Entanglement was established between two single photons with an average two-photon count rate of 1.1 HZ and fidelity of 0.869 ± 0.085.In 2019, Chen et al [118] demonstrated that by combining over 700 fiber QKD links with high-speed satellite networks connected to ground stations covering more than 2000 kilometers, an average secret-key rate of nearly 48 kb s −1 could be achieved.This was almost over 40 times greater than any result achieved previously.This experiment also revealed the possibility of extending a QKD network to a remote node over 2600 kilometers away through a ground-satellite connection (satellite-based QKD is discussed in more detail in Section 2.4.2).The rapid progress in demonstrating quantum teleportation across increasingly large distances via satellites is an exciting development that could have important implications for the energy sector, such as satellite-based greenhouse gas monitoring and quantum navigation, examples which are discussed in more detail in Section 3.
Despite these achievements in satellite-based quantum teleportation, environmental challenges are still being addressed and mitigated.For example, losses in optical channels may lead to Gaussian entanglement loss and, hence, the reduction of different performance figures of merit.Hofmann et al. [119] studied theoretical quantum teleportation protocols under the influence of fluctuating atmospheric losses using the CV approach.This study of the effect of fluctuating atmospheric loss channels on the Braustein-Kimble (BK) protocol indicated that introducing additional losses in the system could improve the teleportation fidelity under certain circumstances, an important finding for developing strategies for improving quantum communication in "real-world" conditions.

QKD Basics
Quantum random number generators (QRNGs) and QKD are first-hand realizations of quantum communications protocols proposed in the mid-1980s. [120]QKD is a method of quantummechanically generating a secure key for encrypting classical information to be sent.115d,120,121] QKD can be achieved with the finite-dimensional Hilbert space such as qubit systems with key information encoded in polarizations, phases, or time bins, or with CVs such as bosonic modes of electromagnetic fields, which are described by an infinite dimensional Hilbert space.To generate the secure key in DV-QKD, single photons or entangled photons need to be created, which are then sent through an optical fiber or free space channels and detected at the other user by means of single-photon detectors.In the case of CV-QKD, the difference is that squeezed coherent photon states are created, which are then detected using homodyne or heterodyne coherent techniques.Here we briefly describe both techniques.

Discrete Variable QKD
Overview: A qubit is written as a vector in 2D Hilbert space spanned by the basis A pure state can be written in a form as where the polar angle  ∈ (0, ) and the phase angle  ∈ (0, 2).Corresponding to  = 0, ,  2 , and  2 we can identify four states in the form These states are related to BB84 protocols, an example of DV-QKD, and are the eigenstates of the Pauli  x and  y matrices.It should be noted that the phase and polarization angle (, ) dependence of the state |⟩ are the most prominent ways of encoding the information in QKD.11b] In 1992, Bennet et al. [122] proposed the BB84 protocol along the same lines as E91, and in later years more advanced protocols were developed. [123]n the BB84 protocol 275 a quantum key is generated as follows: the sender transmits millions of polarized photons over a fiber network.Each photon's polarization state depends upon the bit value (0 or 1) and the basis (e.g., rectilinear or diagonal), both of which the sender randomly selects.The receiver uses a beam splitter to read out the photons' polarization state and decodes the bit value with a basis randomly selected for each photon.The sender and receiver transmit the basis they used for each photon to each other (over a classical channel).For approximately half Figure 9. a) Schematics of the experimental setup for secret QKD over 420 km of ultra-low loss optical fiber using a decoy state.b) Experimental measurements for the secret key rate are indicated by circles. [130]Triangles denote the simulation of an idealized BB84 protocol with the same block sizes as the corresponding experimental points.Squares denote the results of QKD experiments from (1), [131] (2), [132] and (3). [133]Reproduced with permission. [130]Copyright 2018, American Physical Society.
the number of photons the sender and receiver would have used the same basis, and the bits encoded in the photons' polarization state are retained as the quantum key.The rest of the bits are discarded.If the photons are intercepted and resent during transmission all information about their initial polarization is lost, and the bit values measured by the receiver will have errors.The receiver and sender can compare a predetermined subset of the quantum key to detect interception.The BB84 protocol (vide infra) can be extended to a six states basis to enhance the key generation rate and the tolerance to noise. [124]Instead of using two or four states, the six-states protocol uses six states in three basis X, Y, and Z.More detail on different quantum communication protocols and their implementations can be found in reference. [125]xperimental Realization: Realizing the original BB84 protocol requires perfect single-photon sources, generating a single photon at a time.Using a coherent source of more than one photon may impose a security threat due to photon splitting attacks (PSA), which have been demonstrated to exploit incorrect assumptions in security proofs. [126]Despite the different encoding schemes, almost all DV-QKD schemes have single-photon detectors in common to detect the quantum states.
Using a decoy state, the QKD distance and security can be significantly increased for attenuated coherent laser pulse sources, making the decoy state potentially more practical compared to single-photon sources.In 2006, the first decoy state implementation was achieved by modifying the commercially available twoway idQuantique system. [127]In subsequent years, a two decoy state BB84 protocol was realized. [128]In one demonstration, [129] phase encoding was employed, and a secure key was generated over 107 km using optical fiber on a spool, with a secret key rate reaching 12 bit s −1 .A record high secret key distribution distance of over 420 km with a decoy state was achieved using ultra-lowloss (0.17 dB km −1 ) optical fiber (Figure 9). [130]This was achieved with the system clock set at 2.5 GHz and using an efficient superconducting detector with a dark count rate below 0.3 Hz.
The birefringence effect in long-distance optical fibers may introduce problems when information is encoded in the photon's polarization in DV-QKD.Secret information can be encoded in the phase of photons using two sequential laser pulses.Such a technique was reported in 2004 over a 20 km optical fiber. [125]sing 2 GHz sinusoidally gated avalanche photodiodes, a high secret key rate of 24 kb s −1 was achieved over 100 km. [134]The key rate transfer distance was later increased to 260 km using a Michaelson interferometer with two unequal arms connected to a superconducting detector. [135]ecently, twin-field QKD (TF-QKD) has emerged as a promising technique for implementing QKD protocols over long distances without the need for quantum repeaters.Here, the ratedistance limit of QKD is overcome via the use of phase-random optical field pairs that are generated at two separate places and then combine at a central location for measurement.Twin fields, which have the same random optical phase, are then used to extract a quantum key. [136]This technique has engendered multiple demonstrations of QKD over distances greater than 400 km, [137] including optical fiber demonstrations of up to 833 km in a laboratory setting [138] and over 500 km in metropolitan environments. [139]The twin-field approach has the potential to achieve a key rate that scales with the square root of transmittance and can surpass the distance limit of existing QKD protocols.
Satellite-Based DV-QKD: Just as satellites are an attractive technology for implementing long-distance quantum teleportation, discussed above in Section 2.3.4,they play a critical role in long-distance studies of QKD protocols.The space around Earth provides ideal channels to establish a secure key link between satellite-to-ground or satellite-to-satellite stations and vice versa, acting like a vacuum and minimizing photon loss. [140]After a concept proposed initially to establish spacebased quantum communication, [116a,141] a number of studies were conducted at the International Space Station (ISS) and standalone satellites. [142]In 2015, the Matera Laser Ranging license. [125]Copyright 2020, The Optical of Society (OSA).b) Link efficiencies for direct transmission through telecommunication optical fibers (red) and the satellite-to-ground approach (blue).Compared to direct transmission, the satellite-to-ground approach obtained a link efficiency about 20 times higher when the satellite was at 1200 kilometers.115d] Copyright 2017, Springer Nature.
115a] The space link losses were measured as shown in Figure 10a.This scheme was also proposed for QKD with very compact payload transmitters and modulators.Significant photon loss can occur during transmission, depending upon the wavelengths, distance between the stations, and the telescope's aperture diameter.
Low-earth orbit (LEO) satellites, which are around or below an altitude of 2000 km, are optimal for quantum communications due to a low level of exposure to ionizing radiation, relative ease of access and a shorter rotation time around the Earth.LEO was initially considered for quantum communications in 2007 [143] and in the same year, its feasibility was studied for the QKD protocol. [144]The satellite Micius, launched by the Chinese Academy of Science in 2016, is equipped with a quantum optics lab and is not only capable of generating and transmitting coherent and entangled photon states but also of receiving such photons from the ground station. [117]Using this satellite, entanglement-based downlink QKD was also demonstrated via violation of Bell inequalities between Delingha and Lijiang.Because bright light during the daytime increases loss over long-distance transmission, ultralow-noise up conversion single-photon detectors were used at 1550 nm wavelengths to minimize disturbances due to daytime sunlight, and intersatellite QKD over 53 km was achieved. [145]In a groundbreaking study, [146] satellite-based QKD was established over 7600 km, linking China and Europe.Micius has been used in multiple studies to establish secure key links as shown in Figure 10b.For example, Liu et al [121] experimentally demonstrated TF-QKD distribution through sending or not sending protocols.In 2021, Pan and co-workers developed a network capable of quantum communication across 4600 km.The network had two satellite-to-ground QKD links, over 700 fiber QKD links, and over 2000 km of ground fiber network, linking four metropolitan areas. [118]A more detailed review of quantum experiments using the Micius satellite is provided in reference. [147]hile implementing transmitters in a satellite or ground station is possible, the detrimental impact of the Earth's atmosphere on the secure key exchange is asymmetric for a transmitter in a satellite (downlink) and a transmitter on the ground (uplink).This causes photons emanating from the transmitter at the ground to immediately suffer from atmospheric impact resulting in nonuniform phase modulation.Conversely, photons emanating from the satellite transmitter largely travel through vacuum at the beginning and suffer from exceptionally high air density at the final 10 km, which usually results in diffraction.

Continuous Variable QKD
Overview: CV systems are described by infinite-dimensional Hilbert space.One-way CV-QKD protocols can be classified according to the states used (such as coherent or squeezed), the type of encoding implemented (such as Gaussian modulation or discrete alphabet), and the measurement approach used (such as homodyne or heterodyne).Of those, Gaussian protocols have been increasingly used because they are frequently produced in laboratories and are relatively easy to study.In 1999, Ralph [148] first implemented QKD using quadratures of bosonic fields.Cref et al. [149] used quadratures of squeezed beams and encoded a Gaussian-distributed secure key.In 2002, Grosshans and Grangier [150] also implemented Gaussian quadrature modulation and showed its security against attacks, and several subsequent studies [151] also demonstrated the security of CV-QKD against Gaussian attacks.In the two-way protocol [152] Alice and Bob use twice the number of insecure channels and share a key, unlike in the one-way protocol.Any eavesdropper is required to attack both forward and backward channels to steal transmitted Figure 11.a) A schematic for long distance CV-QKD using optical fiber.A coherent pulse of 1500 nm wavelength at 1 MHz frequency was phase and amplitude modulated with Gaussian distribution.The homodyne technique was used to detect the pulse at the receiving terminal.153a] The red triangle, circle and square are from reference. [157]153a] Copyright 2013, Springer Nature.
information.Therefore, a two-way protocol is relatively secure because it promises less chance of information theft.
Experimental Realization: Most CV-QKD schemes are limited to proof-of-concept lab-scale experiments, although some are currently being implemented in "real-world" conditions.As described previously, the Gaussian modulation approach has been widely integrated into existing telecommunication technology.CV-QKD is shown to be highly robust against general attacks but is limited to short transmission distances. [153]A transmission length of up to 80 km was achieved with the highest level of secure key distribution using optical fibers and, as shown in Figure 11, CV-QKD has also been realized in up to 100 km optical fibers. [154]After the very first realization of a Gaussian-modulated CV-QKD protocol in 2003, [155] a number of follow-up studies were conducted, mainly based on telecom components that constituted combined optimized error correction schemes and comprised several active feedback control systems to enhance the mechanical stability. [153,156]V-QKD has also been achieved using measurement-deviceindependent QKD (MDI-QKD). [158]In the CV approach, both Alice and Bob prepare Gaussian-modulated coherent states and send them to an untrusted party, called Charlie.Charlie measures the correlation between the incoming quantum states.When high-efficiency homodyne detectors are used, CV MDI-QKD requires an asymmetric configuration, where Charlie must be located sufficiently close to one of the parties. [159]The key rate drops to zero for channel loss above 6 dB in a telecom fiber; therefore, DV MDI-QKD is the only reliable option currently available. [160]espite many challenges, CV MDI-QKD has a very high key rate potential over a relatively short communication distance.
More advanced CV-QKD technologies are in development. [161]n previous generations, a phase reference, also called the local oscillator (LO), was generated at the transmitter location and thus co-propagated with the signal in the optical fiber.In contrast, the current generation is based on LO generation at the receiver station.

Commercially Available QKD
One early application of QIS was realized in 2004 by several professors at Vienna University in collaboration with Seibersdorf research, who used the QKD protocol in bank transfer applications in Vienna, Austria. [162]In 2007, ID Quantique, [163] based in Geneva, Switzerland, implemented QKD to transmit ballot results to the Swiss capital during that year's national election. [164]D Quantique has continued to develop commercially available devices based on QKD ever since.Its devices such as the Cerberis and the Clavis QKD platforms are commercially available and designed for data center applications including disaster recovery, distributed networks, and key distributions.Currently, multiple QKD companies are located throughout the world, with new market entrants each year: devices developed by QuantumExchange based in Maryland, USA, [165] can execute QKD protocols and generate keys for secure data transmission.Its Phio QK hardware is commercially available and is capable of secure key transmission.Similarly, MagiQ Technologies based in Massachusetts, USA, made its commercial QKD devices available in 2003. [166]ustralia-based QuintessenceLabs also has commercially available quantum-enhanced cyber-secured devices, [167] while the Canadian company Quantropi, Inc. (founded in 2018) has also entered the QKD security space. [168]SK Telecom, a Korean company, uses ion trap quantum repeaters for QKD technologies. [169]apan-based Toshiba Corporation represents another high-profile entrant into the QKD market, [170] demonstrating the fabrication of a QKD device on a semiconductor chip, which represents a significant step toward scalable production. [171]Other significant industry players include QNu (India) [172] and fiber-QKD company SpeQtral (Singapore). [173]Notably, in 2020 Verizon successfully conducted a test run of QKD in the Washington, DC area for secure data transmission, making a promising step toward commercially feasible deployment. [174]Today, quantum communications and cryptography systems are used in several places including banks, corporations, government agencies and other commercial institutions. [175]This quantum technology's maturity is highlighted by the fact that QKD has been commercialized for nearly two decades, has been demonstrated in a variety of commercially viable applications, and is currently available using various platforms produced by different companies around the globe.Moreover, faster and more secure QKD systems are expected to be available soon that rely upon the satellite-based quantum communication systems, which should further accelerate commercialization and widespread adoption.

Quantum Transduction
Quantum transduction is the process of converting one form of energy to another by exciting a quantum state. [176]Quantum transduction allows a seamless exchange of quantum information between two different systems operating at different energy scales and in different physical environments.Solid-state qubits, such as the NV centers in diamond, spins in quantum dots, and qubits in superconducting materials process information at microwave frequency for gate and circuit operations within quantum devices.Establishing communication over a distance between two quantum devices requires information to be sent in the infrared frequency range to avoid loss.Multiple experiments show that fiber optics allow efficient transfer of information in the infrared regime over 100s of kilometers without significant loss. [130,133,177]By processing quantum information with photons in the microwave regime along optical fibers the DiVincenzo criteria for quantum sensing can be realized, and computing and communication is achieved using quantum transducers to convert the photon frequency. [178]This essentially provides a hybrid system with seamless coupling of microwave photons to the propagation modes in fiber optics.After successful demonstration of optical frequency conversion in 1992 by Huang and Kumar, [179] the frequency conversion technique has been established in many quantum networking experiments and in superconductivity where microwave-to-microwave conversion is often implemented.
In quantum transduction involving optical-to-microwave frequency, conversion poses a few challenges.First, the lightmatter interaction is completely off-resonant, with five orders of magnitude difference between the optical and microwave energy.Second, the intermediate states inside a nonlinear material are required to couple these two off-resonant photons with a large energy difference, which requires the development of quantum systems in a new regime of strong nonlinear optical interactions.Experimentally, it is possible to drive the mode using a laser coherently to bring the system into a parametric oscillatory mode.Fundamentally, information to be sent out to the transducer is encoded in a set of bosonic operators <a i >.A transducer is required to faithfully convert the encoded information to another set of bosonic operators <b i >.These operators can be practically disjointed and can represent different types of modes such as photons and phonons.Two different modes can be effectively coupled by driving the intermediate mode with a laser.Then the Hamiltonian for the driven system can be written as [176] H where Ω is Rabi frequency proportional to the coherent oscillation and g eff is a constant that denotes the coupling strength between the optical and microwave modes described by the operator â and b.A variety of intermediate systems that couple these two different modes in a quantum transducer have been proposed to date.One example is atomic ensembles that use nanophotonic coupled-resonators for microwave-to-optical conversion with a photon conversion rate up to 5-515 kHz. [180]Ensembles of atomic systems have modes for optical and microwave excitation, which can be obtained in a variety of gas systems, such as ensembles of neutral atoms, ensembles of trapped ions, and solid systems such as NV centers in nanodiamond and rare earth element (REE)-doped optically transparent crystals.Ensembles of neutral atoms trapped magnetically or optically provide a safe environment to host optical and microwave modes. [181]These modes are coherently excited by generating optical nonlinearities required for microwave-to-optical photon transduction.Usually the electric dipole moment in an optical transition is much stronger.The microwave coupled to the atomic ground states has a weak magnetic dipole moment.These different types of excitations have a large frequency difference, which makes it difficult to couple them coherently.Typically, this challenge can be overcome by using Rydberg states that have microwave electric dipole-allowed transitions, which have strong dipole moments.Rydberg states can couple atomic systems with microwaves. [182]182b] Microwave transitions between Rydberg states in cold and trapped atoms are experimentally achieved in four-wave or six-wave mixing.Transitions between Rydberg states have strong electric dipole moments and are proportional to n 2 , where n is the principal quantum number.The magnetic dipole moments in the GHz regime for S-P transitions scale as 1∕n 3 .Therefore, coupling between two levels in Rydberg states are eventually tuned by selectively exciting them.Reference [183] considered the theoretical model of a cesium (Cs) atom that interacts with a superconducting microwave resonator and an optical cavity.The proposed device consisted of a Cs atom trapped by an optical cavity in a superconducting resonator, as shown in Figure 12a.The atom was coherently converting photons between the microwave resonator and the optical cavity, and the device could transfer quantum information on the order of Mega-qubits per second.The strong dipole moment of up to 1000 ea o , where e is the A single cesium atom trapped in a superconducting resonator (a).Two mirrors on each sides of the atom form an optical cavity. [183]The atom coherently couples both the resonator and cavity and converts the photon's frequency.Electronic levels of the cesium atom can couple both optical and microwave photons by selectively exciting the atom in a certain quantum number.A cesium atom optically pumped to one of the high quantum number levels (n ≈ 90) can resonantly couple with a 5.04 GHz microwave field from 90s to 90p levels (schemes b and c represent one and two ground levels, respectively).The 90p level undergoes an optical transition to 7s, in Figure b, by emitting a photon in the visible frequency and eventually relaxes to the corresponding ground level.This completes a cycle that combines both the excitation and relaxation processes of the atom.Reproduced with permission. [183]Copyright 2017 American Physical Society.
elementary charge and a o is the Bohr radius, between Rydberg levels in a single atom provided a coupling strength of nearly 1 MHz at a distance of 5 m.A Cs atom optically pumped to one of the high quantum number levels (n ≈ 90) coupled resonantly with a 5.04 GHz microwave field from the 90s 1/2 to 90p 3/2 level is shown in Figure 12b,c (schemes b, and c represent one and two ground levels, respectively).The 90p 3/2 undergoes an optical transition to 7s 1/2 by emitting a photon in the visible frequency range and eventually relaxes to the corresponding ground level.This completes a cycle combining both excitation and relaxation.Device effectiveness and fidelity were essentially determined by the atom's coupling strengths to the cavities.In reference, [183] Grad et al also showed that when using a 70 m optical cavity and a 10 m microwave resonator to trap a Cs atom, the atom-optical cavity and atom-microwave cavity coupling strengths were calculated to be 2 × 3 MHz and 2 × 100 MHz, respectively.
Transparent crystals doped with REE ions are another efficient platform to engineer transduction.One potential candidate material is Er 3+ -doped yttrium orthosilicate (YSO) crystals due to their transition occurring within a telecom wavelength (1536 nm). [184]r 3+ has a half-integer spin and has doubly degenerate ground and excited states.An external static magnetic field can lift the degeneracy by potentially generating microwave transitions in the form of magnetic dipole transitions, which are several orders of magnitude weaker than electric dipole transitions, thereby requiring high quality factor (Q) resonators and large ensembles.
A popular, and perhaps the most common, optical-tomicrowave transduction method is based on coupling optical light to the mechanical motion of the LC circuit by using electrostatic forces generated in the capacitive circuit.This type of transduction device is called an opto-mechanical transducer.The microwave interacting with the LC circuit exerts a mechanical force on the nanomechanical resonator, slightly pushing its boundaries, which can be coupled photoelastically to the optical photons.An opto-mechanical transducer consists of a mechanical oscillator with a vibrational mode M, which is coupled to a superconducting microwave resonator ∁ 1 with frequency  c,1 and an optical cavity ∁ 2 with frequency  c,2 as shown in Figure 13a,b.A Hamiltonian that describes this system can be written as [185] Figure 13.An oscillating mechanical resonator M can coherently couple microwave (∁ 1 ) and optical (∁ 2 ) cavities with respective frequencies  c,1 and  c,2 (a).Parameters g o,j gives the strength of coupling between the resonator and the cavities.The density of states (DS) of the modes for the mechanical resonator and cavities are depicted around the mode frequencies for each.A mechanical oscillator coherently couples both cavities by generating microwave-to-optical transduction with a conversion efficiency of . [176]Reproduced with permission under the terms of the Creative Commons (CC BY) license. [176]Copyright 2020, IOP Publishing Ltd.191a] Copyright 2021, American Association for the Advancement of Science.
where b is the annihilation operator for the mechanical oscillator M and âj is the annihilation operator for the resonator j whose coupling strength with the oscillator M is g o,j . j is the amplitude of the external driving force in the LC circuit with frequency  d,j .This Hamiltonian can be used to calculate the photon conversion efficiency between the mechanical resonator and the optical cavity.The conversion efficiency depends on the resonators' damping rate and internal losses.

Microwave Quantum Communication
So far we have mainly focused on of quantum communication examples in the optical/telecom wavelength domain.An intriguing possibility would be an implementation of the described concepts in the microwave range since all the fundamental photon properties hold regardless of frequency. [186]ndeed, because wireless communication is by far the largest form of mass communication currently, there is significant existing infrastructure that could be exploited for microwave-based quantum communication.Additionally, a large amount of microwave quantum research has been primarliy spurred by quantum computing using superconducting circuits and therefore there are several existing microwave devices and platforms required for implementation of scalable microwave quantum communications.
From an energy sector perspective, the potential for bringing secure communications to remote areas devoid of optical infrastructure, such as deep mines, oil and gas platforms, and nuclear reactor cores is very attractive and, potentially, easily implemented via short range secure microwave quantum communications. [187]Another attractive avenue is quantum illumination using microwave photons which can boost radar limits of detection beyond classical limits. [188]he main challenges in the microwave domain come from the requirements of cryogenic hardware operation and ease of implementation of single photon detectors.These challenges have been to a large degree alleviated using schemes for nondemolition detection of single microwave photons, [189] however, they remain confined to a cryogenic regime of operation.Microwave quantum photonics [190] potentially may offer a possibility for room temperature operation due to the existence of high efficiency optical single photon detectors, but whether this would be an experimentally feasible route remains unclear.
A number of experimental realizations of microwave quantum communications have been reported recently. [188,191]As an example, Figure 14 shows the experimental topology for a microwave entanglement swapping demonstration.Here the traditional quantum teleportation and feed forward scheme has been realized using superconducting elements.

Quantum Networking for Energy Applications
With the advent of QIS, quantum networking opportunities for safe and secure energy production, processing and delivery will surpass the opportunities offered by existing networking systems.For example, one long-term opportunity for quantum networking is to assess global CO 2 emissions (Section 3.1).Networked quantum sensors will similarly be critical for monitoring the integrity of fossil energy infrastructure (Section 3.2) and will also play a significant role in both oil and gas exploration, while quantum communication protocols will help ensure the security of the electrical grid as it expands (Section 3.3).Moreover, quantum communication networks can be significant for secure optimization of interdependent energy infrastructure (Section 3.4).Different protocols for enhanced privacy based on quantum entanglement [192] and QKD [193] are proposed, and these proposals form a foundation for building securityenhanced quantum smart grids (Section 3.5).Secure transmission of big data based on lightweight quantum cryptography offers opportunities for directly applying quantum laws in environments relevant for power grid applications.It is possible to combine the mechanisms of one-time pad with QRNGs and QKD protocols to ensure the security of key distribution and design a new lightweight stream cipher quantum technology for power data transmission. [194]Section 3.6 discusses privacy enhanced protocols based upon QKD to prevent disruptions to the energy supply from outside attacks, [195] while Section 3.7 focuses specifically on opportunities in the nuclear energy sector.These and other energy sector-relevant application areas will be discussed within this section, providing an overview of how quantum networking is currently being deployed while also providing an outlook for future areas of need that quantum communication might address.

Assessing Actual Data on Global Greenhouse Gas Emission
Measuring global CO 2 emissions relies upon a network of monitoring stations and sensors around the world, [16] with satellite monitoring in particular playing a prominent role in greenhouse gas mapping. [196]For instance, NASA launched the Orbiting Carbon Observatory-2 (OCO-2) in 2014 to analyze global atmospheric CO 2 emissions at a 1-3 km resolution. [197]ntegration of QIS with satellites (see, for instance, Sections 2.3.3 and 2.4.2) will be essential for global greenhouse gas monitoring.Satellites have played an important role in monitoring gases such as methane from the oil and gas industry and determining the effectiveness of mitigation techniques, though challenges remain, including the need for improved spatial and temporal resolution and mitigation of environmental factors that create uncertainty in measurements. [198]In fact, NASA's carbon monitoring system currently uses both conventional satellite technology and quantum sensing techniques such as quantum light detection and ranging (LiDAR) for emissions monitoring. [199]oreover, the development and deployment of lower-cost miniaturized satellites for QKD is also being actively explored, which could improve the commercial viability of quantum technologies. [200]Quantum communication between satellites and ground stations has been demonstrated and is an ongoing area of research that could eventually be applied to monitoring greenhouse gases. [201]The secure transmission of everincreasing amounts of data collected by sensors around the world will benefit significantly from the development of wireless quantum networks, [202] which will aid in efforts for emission monitoring.Continued exploration of satellite-to-ground QKD [115d,118,203] and the circumvention of barriers such as weather-based disruptions [204] will play crucial roles in comprehensive greenhouse gas assessments.Quantum networking can also be implemented with quantum sensors to remotely monitor oil and gas infrastructure for gas leaks.For example, NV centers integrated in a specially engineered waveguide with an enhanced photon interaction via all-optical schemes [205] can be used at the sensing location, and information about changes in the interaction can be read remotely with single-photon detectors as the information is transmitted via quantum communication.In addition, monitoring carbon emissions from various sources on a regional and global scale can be achieved with enhanced resolution using satellite quantum communication.

Fossil Energy Infrastructure Automation
Fossil energy infrastructures, such as pipelines, [206] geothermal wells, [207] transformers, [208] transmission lines, [209] wellbores, [210] and power plants [211] rely upon high performance sensors to monitor parameters such as corrosion, [212] temperature, [213] humidity, [214] pressure, [215] and greenhouse gas emissions. [216]hese sensors play a crucial role in the automation of energy production, distribution, and consumption, [217] requiring communication between sensors and system controls. [218]Such tasks pose significant challenges, particularly given the harsh environments (e.g., high temperature/pressure, corrosive agents, etc.) often encountered in fossil energy-based applications. [219]Thus, automation in fossil energy infrastructure creates both exciting opportunities and daunting challenges for quantum networking.7a] Networked quantum sensors promise to open new doors in applications such as quantum multiparameter estimation [220] and improvements in sensitivity and performance. [221]However, a need exists for robust quantum materials, platforms, and techniques that are capable of operation in the harsh conditions typically encountered within the energy sector.Importantly, efforts are underway to evaluate potential vulnerabilities in proposed quantum networks to outside attacks [222] and to develop protocols and strategies to defend against potential attacks. [223]

Oil, Gas, and Electricity Infrastructure Build-Out and Planning
Oil and gas exploration relies upon sophisticated navigational equipment and has used satellite-based systems for over half a century to report the precise location of potential fuel deposits. [224]115b,225] Moreover, particularly intricate and rugged equipment are needed for underwater oil/gas exploration, where technologies such as robots, autonomous vehicles, and sensors must operate under high pressure and corrosive environments. [226]7a] Developing a quantum network of clocks has been a broad goal of QIS researchers for precise navigation that would be highly beneficial for oil and gas exploration. [227]nderwater sensor networks are also used to monitor subsea oil and gas infrastructure for energy production and transport. [228]Techniques such as QKD can ensure the safe dissemination of sensor information, and this potential has motivated research into underwater quantum communication. [229]or example, a 2019 study by Ren and co-workers successfully implemented a QKD protocol through 0.5 meters of seawater. [230]he same year, Jin and co-workers successfully transmitted a blue-green photonic polarization state across a distance of 55 m in seawater [231] and the same group later demonstrated a successful underwater QKD protocol at a distance of 30 m. [232] Quantum communications between two submarines has been theoretically explored by Gariano et al., taking into account variables such as depth, distance, and the presence of chlorophyll. [233]234a] Copyright 2020, Oxford University Press.
Another exciting innovation is the development of mobile quantum networks. [234]One promising example was introduced by Gong et.al. in 2020, when they demonstrated entanglement distribution across a range of 200 m over 40 min using a dronebased system (Figure 15).234a] The same group later demonstrated entanglement distribution at a 1 km range using a two-drone system. [235]wiat and co-workers have similarly explored the use of dronebased QKD systems, [236] a key step toward secure communication between drones, which are widely used in the energy sector for applications such as pollution analysis, mapping abandoned energy infrastructure, [237] and power plant monitoring. [238]ther mobile targets used in QKD demonstrations include hot air balloons, [239] airplanes, [240] and trucks, [241] which all may facilitate quantum communication in remote areas such as mines and oil/gas sites.
The expansion of the power grid, particularly to incorporate technologies such as electric vehicle charging stations, creates new vulnerabilities for cyberattacks, fraud, and information leaks. [242]Quantum cryptography protocols such as QKD will likely play a crucial role in planning power grid buildout [243] and will be similarly important for the secure deployment of driverless vehicles.As self-driving vehicles become more preva-lent, sensor networks (often referred to as vehicular networks) will likely be utilized to communicate important information about each vehicle, such as speed and location, to maintain safe roadways. [244]For both the safety and privacy of each driver and vehicle, this information must be collected and transmitted securely, and security protocols such as QKD and QLV (a process known as quantum location verification) [245] have been proposed for vehicular networks. [246]Both electric and autonomous vehicles will be susceptible to threats such as ransomware, viruses, and spyware during vehicle charging and/or software updates, which could collect unauthorized information or have a detrimental impact on vehicle performance. [247]QKD would reveal any attempted eavesdropping or hacking from unauthorized users.
Moreover, microgrids have become increasingly important for providing energy to remote regions [248] and for incorporating renewable energy resources. [249]Microgrids rely on secure data transmission for reliable, resilient operation, vulnerability assessment, and rapid power recovery in the event of an outage. [250]nfortunately, the communications networks upon which microgrids rely provide access points that are particularly susceptible to cyber-attacks, including false data injections, worms, Trojan horses, and other coordinated attacks that can disrupt service. [251]The anticipated expansion of microgrids in the coming years has motivated demonstrations of QKD in microgrid systems to ensure that information in the grid system is transmitted securely (Figure 16). [252]Quantum blockchain protocols are also being explored for ensuring secure and optimized transactions between multiple independent microgrids. [253]For example, a quantum direct communication (QDC) protocol has been proposed to ensure a secure communications network between microgrids for distributed energy resources (DERs). [254]Unlike QKD, QDC encodes information directly using qubits, and this information is communicated over a quantum channel without the use of a key, [255] which may offer advantages including greater efficiency and speed.QDC networks have been developed for up to 15 users [256] and have been implemented at distances of over 100 km. [257]223a] A supervisory control and data acquisition (SCADA) system is used to coordinate and optimize operations within this grid, however the SCADA is prone to attacks that have a deleterious impact on operations, providing another application area for QKD. [258]

Operational Optimization of Interdependent Infrastructure
Essential infrastructures are increasingly becoming interdependent; for example, transportation, fuel, and power station networks are all dependent upon one another. [259]The interconnectedness of critical infrastructure has important real-world implications, as Buldyrev and co-workers noted in their analysis of a 2003 power blackout in Italy, in which a failure in the power system caused a failure in Italy's internet communication, leading to more power failures, and so on. [260]Research is ongoing to determine best practices for maintaining optimum performance within infrastructure networks, analyzing strategies for periodic network maintenance, [261] rapid recovery following disruptions, [262] cost minimization, [263] and network protection, [264] among others.In that same vein, applying quantum theory to complex networks is becoming an increasingly important research direction that will prevent outages to critical infrastructure. [265]

Electrical Grid Modernization
Quantum communication is expected to increasingly play an important role in the effectiveness and security of smart grids, [266] which will collect and securely disseminate energy usage information from consumers to optimize energy distribution. [267]hus, grid modernization will require optimized metering systems to be deployed at energy consumption sites (i.e., homes, businesses, etc.). [268]Information from energy consumption monitoring may then be used to optimize energy distribution based upon usage trends, thereby increasing energy efficiency and reducing waste. [269]Quantum networking, and QKD in particular, can play a critical role in ensuring information is securely collected and transmitted. [270]For instance, Zhang and coworkers proposed implementing QDC (vide supra) for grid security by integrating both a QDC layer (consisting of quantum nodes and channels) and a classical network layer (consisting of classical routers and channels) with the physical layer of the electrical grid system, allowing quantum protocols (e.g., computing, communication, etc.) to be applied to cybersecurity, secured automation, and other grid applications. [271]Together, these efforts contribute to effective and secure data collection and dissemination, which will improve the efficiency with which energy is distributed.

Quantum Key Distribution for Security and Reliability of Energy Delivery
In recent years, security has become an issue of increasing importance in electrical power grids and other critical energy infrastructure. [272]The current level of optimizations in networks and power distribution planning requires an additional level of protection from security breaches. [273]Devices enhanced with quantum technologies enable the possibility of achieving an unparalleled level of security that cannot be breached even by sophisticated adversaries.QKD [115d] is a particularly exciting quantum innovation for energy security. [274]Indeed, as noted in the previous sections, efforts are currently underway to integrate Figure 17.Illustration of a smart grid system with an integrated power grid and communication network.Notice that QKD protocols are only used to establish secret keys for encryption, but not to encrypt the messages.There are two types of communication channels, namely a classical channel and a quantum channel.The quantum channel is a necessity for QKD protocols.Reproduced under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) license. [280]Copyright 2020, Institute of Electrical and Electronics Engineers.
QKD protocols with smart grids (Figure 17).In 2021, QKD was successfully implemented to authenticate fiber optic communications between an electrical substation and a distribution center separated by 3.4 km.A commercially available QKD system from Qubitekk was used in tandem with a Carter-Wegmen authentication protocol. [258]The same group also demonstrated real-world deployment of a quantum trusted node network consisting of three different QKD systems.The trial lasted for 28 hours on a fiber optic cable used to link a communications center with substations. [275]That same year, Amin and co-workers developed a QKD-based authentication scheme to secure meters in smart grids from cyber-attacks. [276]More broadly, Peng and Chen conducted a performance analysis of QKD for power applications, analyzing impact factors such as transmission distance, wind speed, and data traffic, and ultimately determined that QKD could be effective for power sector deployment. [277]These recent experiments all highlight the promise of QKD integration into the electrical grid for secure data transmission.
In the renewable energy sector, secure communication is critical for energy forecasting, which is an increasingly important topic as the global energy portfolio continues to incorporate more wind and solar sources.Quantum networking can aid in the secure transmission of weather forecasting data, which will aid decision-making for renewable energy production, distribution, and consumption. [278]Critically, cybersecurity will become increasingly important as quantum computers become more prevalent, which will make quantum cryptography particularly crucial. [279]

Quantum Networking for Nuclear Energy
The potential devastation caused by a nuclear power plant meltdown, either via an accident or through a deliberate attack, necessitates precautions to ensure safe operation.One preventative method is to use sensors to continually run diagnostics during powerplant operation and communicate those results to a base station. [281]QKD presents an avenue for ensuring the security of the sensor data from outside attackers. [282]Wireless QKD, which would enable remote operation and could streamline operating costs, has been proposed for secure communication between offsite operators and nuclear reactor facilities. [283]Like other components of energy infrastructure, nuclear power facilities are susceptible to SCADA attacks, and a successful cyber-attack on a nuclear plant could have devastating destructive consequences.Recognizing that the maturation of quantum computers in particular poses a significant risk for successful SCADA attacks, Sampalli and co-workers have developed and modelled a protocol based upon BB84 as a defense against quantum computer-based cyberattacks. [284]7a,287] As quantum sensors in particular become more widespread within nuclear power plants, quantum networking between sensors will become increasingly useful. [220]

Further Opportunities and Challenges
The ever-increasing commercializing of quantum communications devices and protocols is a testament to the sophistication and maturation of technologies such as QKD.Nonetheless, as more advanced classical and quantum computers are developed, potential exists for catastrophic cyberattacks on energy and defense infrastructure that could have severe global consequences.Thus, continued advancement in the field of quantum networking is essential to ensure that cybersecurity protocols remain ahead of any threats.Of particular importance are methods for rapidly discovering and developing new quantum communication protocols, as well as tools for evaluating their potential effectiveness.Moreover, optimization of platforms, materials, and protocols for different applications, such as quantum memory and long-distance quantum communication, is important for accelerating technologies from the research lab into a commercializable technology.
An emerging area of quantum networking research is the application of computational techniques for algorithm and protocol discovery to enhance QIS performance. [9,288]For example, Wallnöfer and co-workers applied machine learning techniques to develop new protocols for long-distance quantum communication. [289]Similarly, Francisco Ferriera da Silva et al. used genetic algorithms to evaluate the performance of different quantum repeater chains for quantum communication across long distances. [290]Machine learning has also been applied to analyze imperfections in QKD protocols, [291] while Monte Carlo methods have been applied for evaluating QKD protocols [292] in real-world environments. [293]The use of computational simulation for the rational design of quantum networks has the potential to accelerate QIS development. [294]Since its inception, ensuring the complete security of quantum communications toward any type of potential hacking attack has been a major challenge, and steady progress has been made in this area over the years. [295]ecuring NIST-approved protocols for secure quantum communications will be a major milestone toward widespread usage and development of these systems.
Beyond the development of quantum communication protocols, the development of rugged, practical quantum networking devices must also continue to progress.In practical communication devices of sizes up to a few centimeters, photons are ideal information carriers due to their long coherence time, weak interaction with the environment, and high speed. [29]Integrated photonic devices should bring together desirable features in terms of efficiency, cost, scalability, and performance required to demonstrate quantum communications successfully.Thus, photonic platforms may be the most promising for developing small quantum communication devices.
Similarly, the choice of a suitable material for quantum memory is crucial, particularly for long-distance quantum communication.Rare earth elements (REEs), in particular the lanthanides (e.g., lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, and lutetium), exhibit unique magnetic, phosphorescent, and catalytic properties (see Refs. [296] and [297] ).REE-doped 2D materials such as transition metal dichalcogenides (TMDs) are emerging candidate materials that potentially work as quantum memory in a long-distance quantum network.Er absorbs and emits light at a wavelength of 1.5 μm, within the telecommunication band, and is therefore optimal to amplify light signals sent through optical fibers.Recent theoretical work explained the nature and origin of defectrelated single-photon emission from 2D WSe 2 TMDs. [298]Because TMDs are CMOS compatible, similar techniques might be developed for implementing single-and two-qubit gates with spins in silicon to impurity spins in TMDs, which is an area that merits additional research and development efforts.
For the continued development of quantum communication protocols, it is important to note that within quantum optics, a hybrid paradigm exists in a symbiotic involvement of states and methods from discrete variable (DV) and continuous variable (CV) domains.The strengths of both can thereby be employed at once; for example, the continuous part takes advantage of the deterministic state preparation and relatively simple integration with existing information technologies, while the discrete side offers a natural photodetection basis and "built-in" entanglement distillation after the losses. [74]Both domains may thus be leveraged for enhanced performance.This is an emerging area of research in quantum networking.
Performances of quantum network scenarios can be evaluated through quantum network simulations to address possible implementation challenges in scaling up quantum networks (such as bottlenecks or the dynamics of the network interacting with systems that consist of sending and receiving circuits).Quantum network simulations could be used to address potential challenges during the design phase by evaluating the merits of various quantum network protocols and architectures, or could be used for assessing real-time performances and troubleshooting of already built networks.Since classical computers are unable to simulate generic quantum systems consisting of hundreds of qubits, reduced models must be effectively employed in quantum network simulations.Meanwhile, metrics along with specifications and measurement methods for parameter acquisitions are needed to characterize quantum network performances including tangle, fidelity, entropy, quantum channel capacity, etc. [299] At present, several existing quantum network simulation platforms have been developed to help in understanding and optimizing quantum network architectures, hardware, topologies, and protocols, as summarized in Table 1. [300]he development of quantum networking simulations, like what has been done for the classical Internet, should be further enhanced and advanced with open-source simulation platforms from contributors around the world.Finally, the continued maturation and commercialization of quantum technologies will naturally accelerate innovation and advancement in the field.Indeed, in late 2022, EPB and Qubitekk announced the EPB Quantum Network, the first industry-led, commercially available quantum network for private businesses, government, and academic facilities. [301]The fiber optic network may be used to test and validate new quantum technologies on an actual quantum network, a crucial step for advancing the field.

Conclusions
The global energy landscape is rapidly evolving, with widespread expansion of renewable energy technologies, electric vehicle deployment, smart grid development, and the increased use of microgrids, among other changes.Minimizing pollutants such as greenhouse gas emissions while meeting global energy demand represents a significant challenge that will require substantial innovations.In our previous reviews, [7] we provided an overview and outlook of the benefits and potential future opportunities for quantum sensing, quantum computing, and quantum simulations for the energy sector.In this review, we discussed the current status of quantum communications and networking and their applications in the energy sector, along with emerging opportunities for innovation to ensure clean, secure, and reliable energy production, transportation, and consumption.
Innovations such as the deployment of electric vehicle charging stations, the development of smart grids, and the expansion of microgrids will require sophisticated sensor networks to record data for optimized efficiency, creating new vulnerabilities for cyberattacks and other disruptions.Quantum protocols such as QKD will be essential for ensuring the secure collection and transmission of data while protecting consumer privacy and avoiding disruptions to the energy supply from outside attacks.Moreover, nuclear power plants are major vulnerability points for potential hacking and terrorist attacks.Current and future nuclear plants would benefit greatly from quantum communication protocols both in external networking/data exchange and securing communication and sensor readouts from remote sensors throughout the plant.Satellite monitoring of greenhouse gas emission and/or gas leaks also relies upon sophisticated sensor networks that must be secured, and this area will benefit from ground-to-satellite QKD development.Continued demonstrations of quantum communication in harsh environments (e.g., underwater, long distances, in variable weather/temperature conditions, etc.) and the development of mobile quantum networks will also be invaluable for the creation of market-ready quantum solutions for the energy sector.Of all the QIS pillars, quantum networking may have the most benefits for the energy sector in the short term, given quantum networking's relative maturity and the number of commercial players already in the market.The ever-increasing amount of data that must be collected and disseminated within the energy sector creates the potential for vulnerability to hackers and other outside attacks, necessitating secure networks and communication protocols, an exciting near-term opportunity for quantum communication deployment.In the longer term, quantum sensor networks will lead to significant increases in sensing performance for applications such as emission monitoring, oil and gas discovery, pipeline integrity, and nuclear powerplant security.The development of new quantum communication protocols, improved simulations of quantum networks, field tests of quantum networks in real-world conditions, and integration of quantum networks with new quantum sensors are areas of innovation that will advance the field considerably, as will new innovations in the area of quantum materials.Critically, communication and collaboration between QIS researchers and energy industry stakeholders will be crucial for ensuring that future innovations meet the practical needs of the energy sector.

Figure 1 .
Figure 1.General scope of this review: Application areas of quantum communications and networking in energy/fossil energy and carbon management with brief concepts for each and a discussion on potential opportunities and perspectives.

Figure 2 .
Figure 2. The number of publications on quantum networks and communications since 1990.Searched from the Web of Science database using keywords as shown in the figure.Data were generated on March 29, 2023.

Figure 3 .
Figure3.a) Integrated silicon chip with a tunable high quality (Q) factor ring that generates pairs of photons by spontaneous four-wave mixing.Reproduced with permission.[42]Copyright 2016, The Optical Society (OSA).Silicon chips built with fiber interconnects between chip A and chip B (b, c) and spiraled sources of photon pairs, and path and polarization encoding qubit converters (d, e, f).Reproduced under terms of the Creative Commons (CC BY) Attribution 3.0 license.[43]Copyright 2014, American Physical Society.

Figure 4 .
Figure 4. (a) Light with wavelength  p = 405 nm is scattered by a static thin diffuser and illuminates a nonlinear crystal of BBO and (a) produces spatially entangled pairs of photons by SPDC; (b) photons' momentum is imaged by an electron multiplied charge-coupled device (EMCCD) camera.(c) Direct photon intensity and (d) probability distribution of photon pairs are also shown.[55a]Black-red and blue-red color bars correspond, respectively, to intensity and intensity correlation measurements.with permission.[55a]Copyright 2019, American Physical Society.A schematic of a SOI chip-scale device consisting of four telecommunications-band photon-pair sources, which produce four photons in superposition (e).A qubit demultiplexer for configuring the superposition into a product of two Bell-pair, a reconfigurable post selected entangling gate (R-PEG) and four single-qubit projection and analysis stages (a Mach-Zehnder type interferometer).Reproduced under the terms of the Creative Commons (CC BY) license.[56]Copyright 2019, Springer Nature.

Figure 7 .
Figure7.(a) Demonstration of the unconditional teleportation of arbitrary quantum states between diamond spin qubits, which are separated by 3 meters.Electronic spins (2 and 3 in figure a) were manipulated by microwave excitations at the ground level.These spins were entangled via a scheme of entanglement swapping.Then nitrogen nuclear spin (1 in figure a) is detected with electronic spin (2) using the Bell measurement.Finally, the electronic spin is teleported via a real-time feed-forward onto the remote electronic spin (3).(b) A schematic of a deterministic Bell state measurement.First, the state is prepared and is Bell detected (A in figureb), which is then fed-forward and is read out.The Bell measurement and spin manipulation at Alice's and Bob's location are indicated separately.(N) refers to the operation acting on the electronic (nuclear) spin.For details, we refer to reference.[69a]Reproduced with permission.[69a]Copyright 2014, American Association for the Advancement of Science.

Figure 8 .
Figure 8. Illustration of a satellite-to-ground set up for quantum teleportation of a single photon.A multi-photon set-up for teleportation at the ground station (Panel 1 A), a schematic for transmitting antenna (Panel 1 B), and the satellite receiver set up, which is similar to a ground acquiring, pointing and tracking (APT) system (Panel 1 C).Reproduced with permission.[117]Copyright 2014, Springer Nature.A set up of the transmitters, receivers, and APT performance for satellite-based entanglement over 1,200 km (Panel 2).A schematic of the transmitter for sending the 810 nm entangled photon beam using an 850 nm pulsed infrared laser.(Panel 2 A).A receiver set up where signals are detected by single-photon detectors (SPDs) (Panel 2 B).Error tracking as function of time (Panel 2 C).The APT tracking starts after the satellite reaches an elevation angle of 5°.The physical distance between the ground stations (Delingha, Urumqi, Lijiang) and satellite varies between 500 to 2000 km.Reproduced with permission.[115e]Copyright 2017, American Association for the Advancement of Science.

Figure 10 .
Figure10.a) Space-link losses as a function of station separation distance.The measurement was performed for two different wavelengths  = 850 nm (solid lines) and  = 1550 nm (dotted lines) at varying telescope aperture diameter.Reproduced under the terms the Creative Commons (CC BY) license.[125]Copyright 2020, The Optical of Society (OSA).b) Link efficiencies for direct transmission through telecommunication optical fibers (red) and the satellite-to-ground approach (blue).Compared to direct transmission, the satellite-to-ground approach obtained a link efficiency about 20 times higher when the satellite was at 1200 kilometers.Reproduced with permission.[115d]Copyright 2017, Springer Nature.

Figure 12 .
Figure12.A single cesium atom trapped in a superconducting resonator (a).Two mirrors on each sides of the atom form an optical cavity.[183]The atom coherently couples both the resonator and cavity and converts the photon's frequency.Electronic levels of the cesium atom can couple both optical and microwave photons by selectively exciting the atom in a certain quantum number.A cesium atom optically pumped to one of the high quantum number levels (n ≈ 90) can resonantly couple with a 5.04 GHz microwave field from 90s to 90p levels (schemes b and c represent one and two ground levels, respectively).The 90p level undergoes an optical transition to 7s, in Figureb, by emitting a photon in the visible frequency and eventually relaxes to the corresponding ground level.This completes a cycle that combines both the excitation and relaxation processes of the atom.Reproduced with permission.[183]Copyright 2017 American Physical Society.

Figure 14 .
Figure 14.Experimental implementation of quantum teleportation with propagating quantum microwaves and analog feedforward.Here, an unknown input coherent state is teleported from Alice to Bob by exploiting quantum entanglement characterized by the two-mode squeezing level ST ≲ S. The feedforward signal is generated by the measurement Josephson parametric amplifiers with the degenerate gain G, in combination with two hybrid rings and a local displacement operation on Bob's side.Plots in dashed boxes represent quantum states in the quasi-probability Wigner phase space spanned by field quadratures p and q.Reproduced under the terms of the Creative Commons (CC BY) license.[191a]Copyright 2021, American Association for the Advancement of Science.

Figure 15 .
Figure 15.Illustration of the set-up for the entanglement-distribution experiment.The drone node distributes the entangled-photon pairs to the Alice and Bob stations through a mobile link.A state projection measurement (SPM) is performed at each ground station and a classical communication link is used for coincidence measurements.BF, band-pass filter; PCS, polarization control system; PMF, polarization-maintaining fiber; SC, source cabin; SPAD, single-photon avalanche detector; TX, transmitter APT; RX, receiver APT; TDC, time-to-digital converter.Reproduced under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) license.[234a]Copyright 2020, Oxford University Press.

Figure 16 .
Figure 16.On-line diagram example of quantum communication deployed in a system of six microgrids (DER: distributed energy resources).Reproduced with permission. [252c] Copyright 2022, Institute of Electrical and Electronics Engineers.

Table 1 .
A List of Quantum Network Simulation Software.