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Physical Review A

Security proof for round-robin differential-quadrature-phase-shift quantum key distribution

Yang-Guang Shan, Zhen−Qiang Yin, Hang Liu, Shuang Wang, Wei Chen, De‐Yong He, Guang‐Can Guo, Zheng‐Fu Han

Published Mar 24, 2022• 2 citations
Publisher

Abstract

By introducing four-phase modulations into round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol, the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol is proposed. According to the security proof of RRDQPS protocol, it is able to tolerate a higher error rate of key bits. However, its performance with a practical weak coherent source is still unknown since that security proof only applies to a single photon source. In this article, we give the security proof for the general $n$-photon RRDQPS protocol, by which RRDQPS with a practical weak coherent source becomes feasible in the experiment. Through numerical simulation, it is verified that RRDQPS protocol has an advantage over RRDPS protocol on transmission distance, especially when the pulse number is small.

DOI
10.1103/physreva.105.032441

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By introducing four-phase modulations into round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol, the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol is proposed. According to the security proof of RRDQPS protocol, it is able to tolerate a higher error rate of key bits. However, its performance with a practical weak coherent source is still unknown since that security proof only applies to a single photon source. In this article, we give the security proof for the general nnn-photon RRDQPS protocol, by which RRDQPS with a practical weak coherent source becomes feasible in the experiment. Through numerical simulation, it is verified that RRDQPS protocol has an advantage over RRDPS protocol on transmission distance, especially when the pulse number is small.
Combining the differential-quadrature-phase-shift (DQPS) quantum key distribution (QKD) protocol and the recently proposed round-robin-differential-phase-shift (RRDPS), the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol has been proposed. However, a security proof of the RRDQPS QKD protocol is still missing and its advantage over the original RRDPS protocol is also unknown. Here, we give the security proof of single-photon RRDQPS protocol, by which we clearly show that, if a single photon source is applied, RRDQPS protocol will overwhelm the original RRDPS protocol in terms of tolerable error rate. More interestingly, our proof gives a unified theory covering the well-known Bennett-Brassard 1984 (BB84) protocol and RRDQPS protocol. Thus, it is confirmed that BB84 protocol is indeed a special case of the RRDQPS protocol.
Recently, a round-robin differential phase-shift (RRDPS) protocol was proposed [ Nature 509 , 475 (2014)], in which the amount of leakage is bounded without monitoring the signal disturbance. Introducing states of the phase-encoded Bennett–Brassard 1984 protocol (PE-BB84) to the RRDPS, this paper presents another quantum key distribution protocol called round-robin differential quadrature phase-shift (RRDQPS) quantum key distribution. Regarding a train of many pulses as a single packet, the sender modulates the phase of each pulse by one of {0, π/2, π, 3π/2}, then the receiver measures each packet with a Mach–Zehnder interferometer having a phase basis of 0 or π/2. The RRDQPS protocol can be implemented with essential similar hardware to the PE-BB84, so it has great compatibility with the current quantum system. Here we analyze the security of the RRDQPS protocol against the intercept-resend attack and the beam-splitting attack. Results show that the proposed protocol inherits the advantages arising from the simplicity of the RRDPS protocol and is more robust against these attacks than the original protocol.
The round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol has attracted intensive study due to its distinct security characteristics; e.g., information leakage is bounded without learning the error rate of key bits. Nevertheless, its practicality and performance are still not satisfactory. Here, by observing the phase randomization of the encoding states and its connection with eavesdropper's attack, we develop an improved bound on information leakage. Interestingly, our theory is especially useful for implementations with short trains of pulses, and running without monitoring signal disturbance is still available. As a result, the practicality and performance of RRDPS are improved. Furthermore, we realize a proof-of-principle experiment with up to 140 km of fiber, which has been the longest achievable distance of RRDPS until now, whereas the original theory predicted that no secret key could be generated in our experiment. Our results will help in bringing practical RRDPS closer to practical implementations.
Quantum key distribution (QKD) allows the establishment of common cryptographic keys among distant parties. Many of the QKD protocols that were introduced in the past, involve the challenge of monitoring the signal disturbance over the communication line, in order to evaluate the information leakage to a potential eavesdropper. Recently, a QKD protocol that circumvents the need for monitoring signal disturbance, has been proposed and demonstrated in initial experiments. Here, we propose an improved version of this so-called round-robin differential phase-shifting (RRDPS) protocol, in which both time and phase degrees of freedom are utilized to enlarge the Hilbert-space dimensionality, without increasing experimental complexity or relaxing security assumptions. We derive the security proofs of the round-robin differential phase-time-shifting (RRDPTS) protocol in the collective attack scenario, and benchmark it against RRDPS for different experimental parameters. Furthermore, a proof-of-concept experiment of the RRDPTS protocol, using weak coherent pulses and decoy state method, is demonstrated over 80 km of fiber link. Our results show that the RRDPTS protocol can achieve higher secret key rate in comparison with the RRDPS, in the condition of high quantum bit error rate.
Among various quantum-key-distribution (QKD) protocols, the round-robin differential-phase- shift (RRDPS) protocol has a unique feature where its security is guaranteed without monitoring the signal disturbance. Moreover, this protocol has the remarkable property of being robust against source imperfections, assuming that the emitted pulses are independent. Unfortunately, some experiments with high-speed QKD systems confirmed the violation of the independence due to pulse correlations, and therefore the lack of a security proof, without taking into account this effect is an obstacle for guaranteeing the implementation security. In this paper, we show that the RRDPS protocol is secure against any source imperfections by establishing a security proof with the pulse correlations. The proof is simple in the sense that we make only three experimentally simple assumptions on the source. Our numerical simulation based on the proof shows that the long-range pulse correlation does not cause a significant impact on the key rate, which reveals another striking feature of the RRDPS protocol. Our security proof is thus effective and applicable to a wide range of practical sources and paves the way to realizing truly secure QKD in high-speed systems.
Round-robin-differential-phase (RRDPS) quantum key distribution (QKD) protocol has attracted intensive studies due to its distinct security characteristic, e.g., information leakage in RRDPS can be bounded without learning error rate of key bits. Nevertheless, its implementation is still far from practical due to the complication of its measurement device. Moreover, on the theoretical side, its security is still not clear in view of error rate. Here, by observing a potential phase randomization in the encoding states, we develop a theory to bound information leakage quite tightly and differently. Besides, the error rate is incorporated to improve the secret key rate, which is significant for the understanding of RRDPS. Based on our novel security proof, the practicality and performance of RRDPS can be both improved dramatically. Furthermore, we realize an experiment up to 140km fiber distance which is the longest achievable distance of RRDPS system until now, while the original security proof predicts no secret key can be generated in our experiment. Our results pave an avenue towards practical RRDPS.