Entanglement assisted communication over the free-space optical link with azimuthal phase correction for atmospheric turbulence by adaptive optics

: To improve the reliability of entanglement-assisted (EA) communication over turbulent FSO channels we propose to perform the optical phase-conjugation on idler photons rather than turbulence affected signal photons and use adaptive optics. We experimentally demonstrate that reliable EA communication over outdoor 1.45 km FSO link, established at University of Arizona campus, is possible in strong turbulence regime

The application of entanglement in the field of classical optical communications is relatively new research area and entails massive potentials in the coming future especially when we desire to establish communication at high data rate with high fidelity and low bit-error rates over turbulent free-space optical (FSO) channels.There are myriads of possible applications in both commercial and defense arenas where we can exploit this quantum advantage including quantum sensing and quantum radar applications [1].
In this paper we propose a new entanglement assisted (EA) communication scheme, which is supported by the experimental results, where we make use of entangled photon pairs to carry information at a data rate of 125 Mb/s/wavelength over a free-space optical (FSO) link affected by the strong turbulence effects.In the proposed EA communication concept, instead of performing the optical phase-conjugation (OPC) on signal photons, commonly done in all papers published so far [1,2,4,5,11,12], we perform the OPC on idler photons instead.This gives several advantages compared to the traditional approach with receive side OPC on signal photons.
(1) Instead of performing the OPC on weak signal photons affected by scattering, attenuation, and turbulence effects we perform the OPC on bright idler photons, which is much easier to do efficiently.(2) The OPC on idler photons can be performed on transmit side, receiver side, or at an intermediate stage, which gives us flexibility for the network design.(3) Because the idler photons are distributed over reliable fiber links, we do not need to worry about efficient FSO-to-SMF coupling.We can facilitate FSO-to-fiber coupling by using the multimode fibers (MMFs) instead, which simplifies the optical receiver implementation in the presence of beam wandering effects.(4) The overall receiver complexity can be further reduced because the MMFs can be used as fiber inputs to the balanced detector.(5) The proposed EA system significantly outperforms the classical counterpart in both back-to-back configuration and in FSO links that are affected by turbulence effects.This paper is the first demonstration of entanglement assisted communication in actual FSO channel affected by turbulence.We demonstrate a clear quantum advantage of the proposed entanglement assisted communication system, performing the OPC on idler photons, over the corresponding classical counterpart.So far the proof-of-concept demonstrations, when OPC is applied on signal photons, have been performed in a back-to-back configuration [5,12].To improve tolerance to atmospheric turbulence effects in strong turbulence we use the adaptive optics [13][14][15][16].We demonstrate that the adaptive optics, which is designed for astronomic applications in weak turbulence, is effective in strong turbulence channels.
In the next sections we will go through the in-depth explanation of various parts, components and processes involved in making these experiments work.The details of the proposed EA communication system, with the OPC on idler photons, including experimental setup, are provided in Sec. 2. Experimental results are summarized in Sec. 3. Relevant concluding remarks are given in Sec. 4.

Terrestrial free-space optical testbed
In classical FSO communication we transmit and receive information by modulating a laser beam or a broadband light beam with our information that is in a forward error correction (FEC) coded modulation format such as on-off keying, BPSK, quadriphase-shift keying (QPSK), quadrature amplitude modulation (QAM), etc.Then this modulated information beam is expanded and by a telescope transmitted toward the receiver over an FSO link.During propagation the beam encounter various atmospheric effects including scattering, attenuation, and atmospheric turbulence effects.At the receiver end the received beam is collected by the compressing telescope and converted into electrical domain by a balanced detector, and after mixing the incoming optical signal with the local oscillator (LO) laser signal.The diagram in Fig. 1 is a block representation of our outdoor entanglement assisted communication experimental testbed showing all the major components and the overall scheme at the University of Arizona main campus.Our experimental setup is comprised of three main stages: namely, the transmitter, FSO stage, and the receiver.The transmitter is further subdivided into entangled photon pair generation module and modulation part.The FSO stage is the free space-optical link including adaptive optics subsystem.The receiver is comprised of balanced detection and offline post processing and calculations.In the next sections we will elaborate more on every stage and sub-stage of this experimental testbed.The physical location of the experiment is the Quantum Communication (QuCom) Lab (ECE room 549), in the Electrical and Computer Engineering (ECE) building at the University of Arizona (UA).In QuCom Lab we have located our optical transceiver along with adaptive optics subsystem that's set up on an optical bench.

Free-space optical link
Figure 2 shows the Google image of the FSO link over the UA campus, showing the FSO link we set up between ECE building and the Optical Sciences (Meinel) building (OpSci).
The way our FSO link is set up is that we transmit our information carrying beam from the ECE Rm 549 toward the OpSci building, which is 725 m away.On the rooftop of Optical Sciences building, we have placed a 5" wide corner-cube retroreflector that returns the beam back toward ECE Rm 549 window, resulting in a link that is 1450 m long as shown in the Fig. 3.
Figure 3 shows the basic scheme of the FSO link between ECE and OpSci buildings.In our FSO experiments we use beam expanders with different zoom capacities depending on building sway and the weather conditions of the day, such as wind direction.Most of the time we use  a 20 × zoom beam expander that gives a beam of about 8" in diameter at the OpSci building's rooftop as can be seen in Fig. 3.
In Fig. 4 we detail the various components of the FSO transceiver in ECE Rm 549 (QuCom Lab).We transmit our beam to free space using a beam expender and a periscope, as shown in Fig. 4. The beam expander points the beam towards a small 2" mirror that functions as a transmitting mirror.Then the beam gets reflected from the common transmitting − receiving mirror and points toward the corner-cube retroreflector placed on the roof of the Meinel building.The reflected, receiving beam uses the common periscope mirror and then the receiving mirror and finally the beam is captured by the receiving/compressing telescope.
The entanglement assisted (EA) FSO communication setup is already shown in Fig. 1.Below we provide a detailed description of the setup.

Transmitter configuration
The experiment begins by generating entangled photon pairs for which we made by using two type-0 periodically poled lithium niobate (PPLN) waveguides, with the first one serving as the entanglement generation source and second one as the optical phase-conjugation (OPC) module.We start with a tunable laser set to 1529.75 nm that's amplified to an appropriate power level with the aid of EDFA and then we split this EDFA's output into 50:50 ratio using a beam splitter.One of the outputs out of the beam splitter is applied to the first PPLN waveguide, serving as the entanglement generation source.Inside the PPLN waveguide the first step that occurs is the second harmonic generation (SHG) where two 1529.75nm pump photons generate a single 768.693 nm photon as illustrated in Fig. 5.
In the second step (see Fig. 5) the 768.7 nm secondary pump photons undergo a spontaneous parametric down-conversion (SPDC Type-0) process and generate entangled photon pairs.Based on the components available to us we selected 1510nm-1550 nm entangled pair, where we choose 1510 nm as the idler and 1550 nm as the signal photons, respectively.The decision to choose these wavelengths for idler and signal photon pairs was made by the wavelength division multiplexing (WDM) demultiplexer available in our QuCom Lab, which is the compact coarse WDM (CCWDM) demultiplexer, which we use to separate the signal and idler photons.
The output of the first PPLN waveguide is given to a CCWDM demultiplexer (demux) to split the idler (1510 nm) from the signal (1550 nm) photons, the CCWDM demux module has different wavelength outputs, which are isolated ranging from 40 dB to 60 dB depending upon their adjacency to each other.Two CCWDM demux stages are needed to suppress residual 1529.75 nm pump signal.The beam composed of signal photons (at 1550 nm) is then applied to a Mach-Zehnder-based I/Q modulator used as the phase modulator (PM).The RF input of the PM is based on an arbitrary waveform generator (AWG).The information applied is a low-density parity-check (LDPC) encoded binary phase-shift keying (BPSK) signal with a code rate for the FEC frame being 0.6225 and recorded in the AWG.The codeword length is 3992 bits with 2497 information bits and 1495 parity-check bits.The LDPC-code we used is girth-10, column-weight-3 quasi-cyclic LDPC code, designed as we described in Ref. [17].We organized our information with 616 extra bits as the 'header' for each codeword, forming an FEC frame.This header is known at the receiver side, and we use it for identifying the start of the frame by a cross-correlation function during the offline signal processing.The output of the PM is then beamed out of ECE Rm 549 as explained earlier.The data rate was 125 Mb/s/wavelength.
The filtered 1510 nm idler photons are mixed with the remaining part of 1529.75 nm from the beam splitter and then applied to the second type-0 PPLN waveguide serving as the optical phase-conjugation module.Inside this PPLN waveguide the 1510 nm idler photons undergo optical phase-conjugation and we select the 1550 nm output using another CCWDM demux.This 1550 nm output is then applied to a 1 km optical fiber serving as the optical delay line (ODL).The main purpose of this fiber is to provide optical delay same as the received signal photons after the return trip to OpSci over the FSO link.The optical fiber has a refractive index of 1.45 and a 1 km long fiber will have almost the same arrival time as if the beam has travelled over 1.45 km in free space.(An interested reader is referred to Ref. [11] for additional details on SPDC and OPC processes.)

Receiver configuration
Once the beam is back in the ECE Rm 549 (QuCom Lab), we make use of compressing telescope with a doublet to collimate and reduce the beam size.The received beam is then made to traverse on the optical bench through the adaptive optics setup before we finally couple it into an optical fiber.This received beam is then converted to electric domain by applying it to a homodyne optical balanced detector.The other input to this detector is our optically phase-conjugated beam that we generated from idler photons.The electrical output of the balanced detector is then sampled at 100GSa/s by a Tektronix oscilloscope.The samples of this electrical (RF) waveform are then transferred to a personal computer (PC) for processing it off-line.We test this waveform information for cross-correlation against the header, that is already known at the receiver, to determine the start of the codeword.Afterwards, we perform the LDPC decoding and compute the bit error-rates (BERs) for both the received signal and after the LDPC decoding takes place.

Adaptive optics subsystem
Our entanglement assisted communication system over the free-space optical link has an additional feature of applying the adaptive optics to compensate the wavefront distortion introduced by the atmospheric turbulent channel.Below in Fig. 6 we can see the image of our adaptive optics setup on the optical table.
In a lightwave line-of-sight based FSO communication link the beam travelling in free-space undergoes atmospheric turbulence effects.The atmospheric turbulence is mainly due to the temperature variations along the optical path in free space.This optical medium gets heated from the ground below, which can be anything such as ground that is covered or uncovered by vegetation, building's rooftop, concrete parking lot, asphalt road, industrial vents, air conditioners vent, water body like river, lake, ocean, etc.All these release heat at different rates and at different times of the day and season.This situation is far worse in urban areas or areas with high daily temperature variations as in tropical, arid, and semi-arid regions.These temperature variations cause changes in refractive indices along the optical path.All these variations are responsible for distortion of azimuthal phase in the wavefront of our information carrying beam [13][14][15].This causes the degradation of the optical beam wavefront, which exhibits the scintillation in the received power as well as the beam wandering effects.The common consequences are poor reception of power, loss of information, and possible outages.
To counter the effects of atmospheric turbulence on our information carrying beam we implemented adaptive optics [13][14][15] as a solution, which is a technology used by earth-based telescopes to collect the light coming from celestial bodies.The light entering atmosphere from space undergoes similar phase distortions only differs in that it traverses the atmosphere vertically down whereas in FSO links, as in our case, is horizontal to the ground.In a typical adaptive optics system as shown in Fig. 7, the beam first falls on a deformable mirror and then its wavefront is observed by passing it onto a Shack-Hartmann wavefront sensor (WFS).The sub-apertures of the WFS create a "spot field" onto the camera of the WFS from which the phase of each sub-aperture is determined by computation.This information is then broken down into Zernike polynomials with appropriate coefficient to each polynomial.Afterward, a fast computer performs calculations that are essential to create a phase-conjugate of the observed wavefront by converting the distorted image into control voltages to the actuator of the deformable mirror.The deformable mirror we are working with can be molded into various shapes by its 140 actuators arranged in square grid that can independently move the individual site on the mirror forward and backward.This adaptive optics setup was built by our group with help from the Boston Micromachines Corporation (BMC).Our adaptive optics feature a 140 actuator Deformable mirror (DM) from the BMC and an 878 frames wavefront sensor from Applied Optical Systems (AOS).Then we send a collimated received beam onto the deformable mirror and after that we split 8% of that beam toward WFS thus, the WFS and DM are operated in a feedback servo loop.This whole process is controlled by our software running on a fast personal computer for all the calculations and making adaptive optics corrections at a rate of 350 + frames/sec.
To improve the outdoor system stability we make use of shock absorbing sorbothene vibration damping sheets under the aluminum breadboard upon which we have mounted the retroreflector.For beam wandering stability introduced by turbulence we have recently implemented a faststeering mirror operated in a closed loop.The current system does not need alignment adjustment for several hours, which is sufficiently stable for proof-of-concept experiments.

Experimental results
To test the performance of our entanglement assisted communication concept we first compared the results against classical lightwave communication.For this we first performed this experiment using an optical fiber in a back-to-back configuration.We generated the entangled photon pairs using the first PPLN waveguide, serving as the entanglement generation source, and selected the signal and idler photons by the CCWDM demultiplexer.We modulated signal photons (at 1550 nm) with our LDPC encoded BPSK information (same as earlier described) and performed phase-conjugation on idler photons.We applied both signal and conjugated idler photons to a homodyne balanced detector and finally computed BER from the samples of the waveform taken from the oscilloscope.We performed this experiment for various average power levels for the signal photons.Similarly, we performed the same experiment by phase modulating a 1550 nm laser signal and detected with help of a 1550 nm LO laser.Below in Fig. 8 we present the BER results against applied averaged power to signal photons in a back-to-back configuration.The phase-conjugated idler photons power has been adjusted by an attenuator for optimum BER performance.To achieve the target BER we organized the transmitted sequence into a packet composed of the required number of LDPC codewords to count at least 100 errors per point.The optimum signal photons-to-phase-conjugated idler photons power was about 2.5, which is significantly lower compared to the classical case with optimum signal-to-LO power ratio being above 10.It is evident from Fig. 8 that the proposed EA communication concept significantly outperforms the corresponding classical counterpart in terms of the receiver sensitivity.
The next plot in Fig. 9 summarizes the uncoded BER comparison of EA communication system against classical lightwave system but this time over our retroreflector based 1.45 km long outdoor, terrestrial FSO link.Experiments were performed on April 19, 2023 in the afternoon hours (the weather was sunny, wind less than 5 mph, humidity 5-6%, temperature 93-96°F).As mentioned earlier, in this case we use an optical delay line to match the optical path of idler photons so that the delay matches that of the signal photons that make the trip over the FSO link.We performed both methods on the same day with the same average signal powers at 3.3 mW, but in different turbulence conditions.The uncoded BER results show that EA communication system for stronger turbulence has a significantly better BER performance over the FSO channel than the classical laser communication system operated over the medium turbulence FSO channel.On the top right side of the plot, we have a histogram of the received power that is averaged for both EA and classical cases.The histogram on the top right was taken while we were collecting classical data, the near Gaussian distribution suggesting medium turbulence regime.The bottom right plot shows the histogram when we ran the EA communication experiment.The Rayleigh distribution of the received power clearly indicates strong atmospheric conditions.Therefore, the EA communication system in strong turbulence regime outperforms the classical lightwave communication system operated in medium turbulence regime.The LDPC decoder corrected all channel errors in both cases.The classical light-wave communication system for 3.3 mW of launch power in strong turbulence has the BER of 0.5 and cannot operate in strong turbulence regime at all.Therefore, in a strong turbulence regime the quantum advantage of EA communication system is clearly evident.Given that the refractive structure parameter C n 2 in urban area is propagation distance dependent we use the received power histograms as the  figure of merit, similarly as in Refs.[15,16].Moreover, the C n 2 parameter does not take the wavelength and propagation distance dependence of turbulence effects.On the other hand, the Fried parameter is applicable in weak turbulence, but not in beyond strong turbulence so that the measured probability density functions of received power are more adequate to use as they take all relevant turbulence parameters into account jointly.In the next plot, Fig. 10, shows a comparison in terms of the uncoded BER when we performed EA communication over an FSO link against results obtained after applying the adaptive optics.The LDPC decoder corrected all errors in both cases.
From the plots we can clearly see better tolerance to turbulence effects when the adaptive optics is used.The histogram plot on the right to the BER plot shows a received power distribution that is between a logarithmic and Rayleigh distribution, suggesting beyond strong atmospheric turbulence regime.Interestingly, even though the adaptive optics is designed to operate in weak turbulence regime, during the night, in astronomy, it can be used to improve the tolerance to turbulence effects in beyond strong turbulence regime for EA communication applications.
The traditional entanglement assisted receiver performs the OPC on receive side [5,12] and a such requires coupling the optical beam affected by strong turbulence into the core of SMF, which is extremely difficult to do with a low-cost design advocated in this paper.Namely, to perform the OPC on signal photons, based on PPLN waveguide, the turbulence affected optical beam needs to be coupled to the SMF to avoid exciting higher order nonlinear spatial modes in the PPLN waveguide.This is the reason why we introduced the scheme in which we perform the OPC on idler photons instead, so that we can use the MMF to couple the beam and free space based balanced detectors as an entanglement assisted detector, which represents a low-cost solution for future FSO applications.

Conclusion
In this experiment, we were able to successfully develop a new method to perform communication that involves LDPC encoded BPSK information using entangled photons.We generated entangled photons pairs by making use of the PPLN waveguide.The process involved here is the second harmonics generation which is followed by parameter down-conversion process that results in generation of a large number of signal-idler photon pairs.We modulated the signal photons with LDPC encoded BPSK information at a data rate of 125Mb/s.We performed optical phaseconjugation on idler photons and used the phase-conjugated idler beam to detect information modulated on signal photons with the help of a homodyne balanced optical detector.We performed BER calculation for the detected signal for uncoded and for LDPC corrected frames.Thanks to our strong LDPC code we did not encounter any BER after performing LDPC error correction in all cases in our experiment such as classical and EA communications, with and without the AO.We tested our proposed entanglement assisted communication concept against the classical lightwave communication demonstrated its superiority in both back-to-back configuration and over turbulent FSO link.
In the back-to-back configuration the EA communication system is superior to the classical light-wave communication in terms of lower power requirement for the communication link to be feasible, in other words it has a better receiver sensitivity.
In communication over the FSO link we compensated for the time delay signal photons arriving at the detector by propagating phase-conjugated idler photons over a 1 km long optical fiber with refractive index of 1.45 to match the delay of signal photons making the round trip over the FSO link in air.The EA communication system operating in strong turbulence has shown lower BERs for the same launch power as in classical lightwave communication system operated in medium turbulence.
Also, from our results we have successfully demonstrated that adaptive optics can improve the tolerance to turbulence effects in the EA communication system even in the beyond strong atmospheric turbulence regime.
To summarize, from our experimental results in terms of BER we were able demonstrate the clear quantum advantage of the proposed entanglement assisted communication system compared to the classical lightwave communication system, especially in strong turbulence regime when the classical communication system was not operational.The AO provided better tolerance to turbulence effects and was operational even in beyond the strong turbulence regime.
Disclosures.The authors declare no conflicts of interest.

Fig. 6 .
Fig. 6.Various components of adaptive optics subsystem as laid-out on the optical table.BS: beam splitter.

Fig. 7 .
Fig. 7.The basic scheme of our implementation of adaptive optics subsystem.

Fig. 8 .
Fig. 8. BER performance of entanglement assisted communication vs. classical laser communication by plotting BER against increasing average signal photons power to detector in a back-to-back configuration for both cases.

Fig. 9 .
Fig. 9.The uncoded BER performance of EA and classical laser communication systems with same average signal photons power (3.3 mW) at launch over the FSO links under different turbulent conditions.The histogram plots for received power show the turbulence conditions.

Fig. 10 .
Fig. 10.Uncoded BER improvements in EA communication system with adaptive optics in strong turbulent conditions for different transmissions over turbulent FSO link.