Fully Passive Quantum Key Distribution

Wenyuan Wang, Rong Wang, Chengqiu Hu, Victor Zapatero, Li Qian, Bing Qi, Marcos Curty, and Hoi-Kwong Lo

Phys. Rev. Lett. 130, 220801 – Published 31 May 2023

Abstract

We propose a fully passive linear optical quantum key distribution (QKD) source that implements both random decoy-state and encoding choices with postselection only, thus eliminating all side channels in active modulators. Our source is general purpose and can be used in, e.g., BB84, the six-state protocol, and reference-frame-independent QKD. It can even potentially be combined with measurement-device-independent QKD to achieve robustness against side channels in both detectors and modulators. We also perform a proof-of-principle experimental source characterization to show its feasibility.

Received 29 November 2022
Accepted 19 April 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.220801

Physics Subject Headings (PhySH)

Optical quantum information processing Quantum communication Quantum cryptography Quantum optics Quantum protocols

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Wenyuan Wang ^1,*, Rong Wang¹, Chengqiu Hu ¹, Victor Zapatero^2,3,4, Li Qian^5,6, Bing Qi ⁷, Marcos Curty ^2,3,4, and Hoi-Kwong Lo^{1,5,8,6,9,†}

¹Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong
²Vigo Quantum Communication Center, University of Vigo, Vigo E-36310, Spain
³Escuela de Ingeniería de Telecomunicación, Department of Signal Theory and Communications, University of Vigo, Vigo E-36310, Spain
⁴AtlanTTic Research Center, University of Vigo, Vigo E-36310, Spain
⁵Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, M5S 3G4, Canada
⁶Centre for Quantum Information and Quantum Control (CQIQC), University of Toronto, Toronto, Ontario, M5S 1A7, Canada
⁷Cisco Systems, San Jose, California 95134, USA
⁸Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7, Canada
⁹Quantum Bridge Technologies, Inc., 100 College Street, Toronto, Ontario, M5G 1L5, Canada

^*Corresponding author. wenyuanw@hku.hk
^†Corresponding author. hoikwong@hku.hk

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Issue

Vol. 130, Iss. 22 — 2 June 2023

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Images

Figure 1
(a) Passive decoy-state setup [10, 11]. The output intensity is determined by the random phase difference between the two sources. Alice postselects the intensity with a classical detector to prepare decoy-state settings. (b) Passive encoding setup [12]. The output polarization is determined by the random phase difference between two sources. Alice postselects the polarization with a phase measurement to prepare BB84 states. (c) Our fully passive source. The output state is a phase-randomized coherent state with arbitrary polarization and arbitrary intensity. Alice can postselect based on observations from her two classical detectors and her phase measurement between the $H$ and $V$ modes. Here, the sources emit strong light, which is attenuated to the single-photon level before being sent out. The same setup is applicable to time-bin phase encoding if we replace the polarizer and the polarizing beam splitter with a delay line and a beam splitter.
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Figure 2
(a) Postselection on intensities $(μ_{H}, μ_{V})$ . The shaded regions correspond to the $Z$ basis and $X − Y$ plane on the Bloch sphere. The slope $x = μ_{V} / μ_{H}$ on this plot determines the latitude (polar angle) $θ_{H V}$ of the state on the Bloch sphere. The postselected regions can further be divided into subregions to implement decoy states. (b) The phase postselection step that determines the longitude of the state, which helps Alice determine, e.g., the $X$ basis and $Y$ basis polarization states. (c) Corresponding states on the Bloch sphere based on the intensity postselection step.
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Figure 3
Examples of additional postselection on intensity or phase distribution by Alice. We can use this technique to, e.g., modify the intensity distributions of $μ_{H}$ or $μ_{V}$ , or to shape a nonuniform but known phase distribution into a uniform one.
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Figure 4
Left: key rate comparison between active and fully passive decoy-state BB84 assuming infinite data size, using the strategy in Fig. 2. The size of the $Z$ basis postselection regions and the maximum intensities are optimized. Right: key rate simulation for fully passive decoy-state BB84 under finite-size effects (considering collective attacks) with different data sizes. A full optimization on all postselection parameters is performed.
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Figure 5
An equivalent setup for a fully passive source using only one single laser. This setup makes use of two delay lines of $Δ t$ and $2 Δ t$ to interfere four independent pulses from different time bins. Here, we need to use a fixed-intensity modulator (or an optical switch) to suppress every three out of four output pulses. Note that this does not leak additional information as a fixed pattern of signals is selected and no random number is used [56].
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Figure 6
(a) Histogram of experimentally observed intensities for the passive decoy module. It follows the theoretical prediction well, implying uniform phase distribution, good measurement accuracy, and good interference visibility. Additionally, the intensity data passed an autocorrelation test, implying randomness of phase distribution. (b) Measured phase $ϕ$ and characterized error $ϕ_{error}$ , showing we can perform accurate phase measurement. Phase measurements are performed by measuring in the $X$ or $Y$ bases (detailed setup included in the Supplemental Material, Sec. J). For simplicity, the passive encoding module is separately tested from the passive decoy module, meaning that here we only create and measure states randomly on the equator of the Bloch sphere.
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