Phase-Matching Quantum Key Distribution Without Intensity Modulation

Shan-Feng Shao, Xiao-Yu Cao, Yuan-Mei Xie, Jie Gu, Wen-Bo Liu, Yao Fu, Hua-Lei Yin, and Zeng-Bing Chen

Phys. Rev. Applied 20, 024046 – Published 18 August 2023

Abstract

Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose an alternative method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bit/s under a 45-dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with a six- or eight-slice random phase, our protocol provides a promising solution for constructing quantum networks.

Received 20 March 2023
Revised 30 May 2023
Accepted 27 July 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.024046

Physics Subject Headings (PhySH)

Optical quantum information processing Quantum cryptography Quantum optics Quantum protocols

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Shan-Feng Shao ^1,§, Xiao-Yu Cao^1,§, Yuan-Mei Xie¹, Jie Gu¹, Wen-Bo Liu¹, Yao Fu^2,*, Hua-Lei Yin ^1,†, and Zeng-Bing Chen^1,‡

¹National Laboratory of Solid State Microstructures and School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
²Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

^*yfu@iphy.ac.cn
^†hlyin@nju.edu.cn
^‡zbchen@nju.edu.cn
^§The authors contributed equally to this work.

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Vol. 20, Iss. 2 — August 2023

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Figure 1
Schematic of phase-matching QKD without intensity modulation. Alice and Bob utilize pulse laser sources to prepare weak coherent states. They use a random number generator (RNG) to generate random numbers for random phases and random key bits. For each pulse train, Alice and Bob exploit a phase modulator (PM) to apply phase $θ_{a} + r_{a} π$ and $θ_{b} + r_{b} π$ on each pulse according to the random phase selection and random key bits $r_{a}$ and $r_{b} \in {0, 1}$ , respectively. A variable optical attenuator (VOA) is used to implement a weak pulse with single-photon-level modulation. An untrusted Eve receives the two pulses from Alice and Bob and then uses a beam splitter (BS) and single-photon detectors to conduct an interference measurement.
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Figure 2
Schematic of the proof-of-principle experiment. Detectors $D_{1}$ and $D_{2}$ are superconductor nanowire single-photon detectors. Detectors $D_{3}$ , $D_{4}$ , $D_{5}$ , and $D_{6}$ , which monitor the intensity of pulses, are photodiodes. All the devices are synchronized by the signals from an arbitrary waveform generator. The pulses are emitted from a homemade laser and reach a circulator (Cir) whose direction is from 1 to 2 and from 2 to 3. Then, the pulse is separated into two pulses by a 50:50 BS, and the two pulses enter a Sagnac loop. Before modulation, the pulse passes through a bandpass filter (BPF) and the BS. Alice and Bob can distinguish whether a pulse belongs to them after time calibration. The two pulses modulated by Alice and Bob passing through the Sagnac loop will interfere with each other by the BS. Polarization controllers (PCs) modify the polarization of the two pulses to maximize the detection efficiencies. Finally, the pulses after interference are then detected by two single-photon detectors $D_{1}$ and $D_{2}$ . Note that the devices covered with the yellow cuboid are not introduced in the implementation.
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Figure 3
Finite-size simulation results of our protocol. The parameters are shown in Table 1. We select data sizes $N = 10^{10}$ , $10^{11}$ , and $10^{12}$ to conduct the simulation.
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Figure 4
We compare the performance of our protocol with phase-matching QKD [36] and four-intensity MDI QKD using the double-scanning method [87]. The simulation parameters are provided in Table 1 with a data size of $N = 10^{11}$ . The phase slice number of our protocol $M$ is set as 6 in comparison. The total security parameter $ϵ_{tot}$ of four-intensity MDI QKD using the double-scanning method is the same for that of our protocol, which is equal to $3 \times 10^{- 10}$ .
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Figure 5
Deviation of the even-photon state in our protocol. We simulate the deviation with the data size $N = 10^{11}$ . The other parameters chosen are shown in Table 1. The deviation of the even-photon state can denote the gap between the continuous random phase and discrete random phase.
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Figure 6
Considering the experimental results, we depict the secret key rate when the data size $N = 10^{11}$ and phase slice $M = 8$ . We implement the experiment with the optimized intensity under 35-, 40-, and 45-dB channel losses.
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