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Physical Review A

Phase-error-rate analysis for quantum key distribution with phase postselection

Yao Zhou, Zhen−Qiang Yin, Yang-Guang Shan, Ze-Hao Wang, Shuang Wang, Wei Chen, Guang‐Can Guo, Zheng‐Fu Han

Published Feb 12, 2024• 2 citations
Publisher

Abstract

Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate serves as a critical indicator of information leakage and directly influences the security of the shared key bits between communicating parties, Alice and Bob. In estimating the upper bound of the phase error rate, phase randomization and subsequent postselection mechanisms serve pivotal roles across numerous QKD protocols. However, the nonzero interval of phase postselection will introduce intrinsic errors, leading to an overestimation of phase error rate. Here we make a precise phase-error-rate analysis for QKD protocols with phase postselection, which eliminates error rate associated with nonzero interval and helps us to accurately bound the amount of information an eavesdropper may obtain. We further apply our analysis in sending-or-not-sending twin-field quantum key distribution (SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation results confirm that our precise phase error analysis can noticeably improve the key rate performance especially over long distances in practice. Note that our method does not require alterations to the existing experimental hardware or protocol steps. It can be readily applied within current SNS-TF-QKD and MP-QKD for higher key rate generation.

DOI
10.1103/physreva.109.022416

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Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate serves as a critical indicator of information leakage and directly influences the security of the shared key bits between communicating parties, Alice and Bob. In estimating the upper bound of the phase error rate, phase randomization and subsequent postselection mechanisms serve pivotal roles across numerous QKD protocols. However, the nonzero interval of phase postselection will introduce intrinsic errors, leading to an overestimation of phase error rate. Here we make a precise phase-error-rate analysis for QKD protocols with phase postselection, which eliminates error rate associated with nonzero interval and helps us to accurately bound the amount of information an eavesdropper may obtain. We further apply our analysis in sending-or-not-sending twin-field quantum key distribution (SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation results confirm that our precise phase error analysis can noticeably improve the key rate performance especially over long distances in practice. Note that our method does not require alterations to the existing experimental hardware or protocol steps. It can be readily applied within current SNS-TF-QKD and MP-QKD for higher key rate generation.
Quantum key distribution (QKD) stands as a pioneering method for establishing information-theoretically secure communication channels by utilizing the principles of quantum mechanics. In the security proof of QKD, the phase error rate serves as a critical indicator of information leakage and directly influences the security of the shared key bits between communicating parties, Alice and Bob. In estimating the upper bound of the phase error rate, phase randomization and subsequent postselection mechanisms serve pivotal roles across numerous QKD protocols. Here we make a precise phase error rate analysis for QKD protocols with phase postselection, which helps us to accurately bound the amount of information an eavesdropper may obtain. We further apply our analysis in sending-or-not-sending twin-field quantum key distribution (SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation results confirm that our precise phase error analysis can noticeably improve the key rate performance especially over long distances in practice. Note that our method does not require alterations to the existing experimental hardware or protocol steps. It can be readily applied within current SNS-TF-QKD and MP-QKD for higher key rate generation.
Twin-field (TF) quantum key distribution (QKD) has been extensively researched because of its long transmission distance. The phase-encoding TF-QKD can realize both a high key rate and a long transmission distance, so it has attracted a lot of attention. In this article, we are inspired by the sending-or-not-sending TF-QKD, in which the information leakages of correct rounds and erroneous rounds are calculated separately. And, we notice that this kind of method has been used in many QKD protocols---for example, the six-state QKD. We apply a similar method to the phase-matching TF-QKD and find some improvement in it. With the new analysis, the transmission distance can be improved without any changes in experiments. We also apply the new analysis in the four-phase partial-phase-postselection protocol, and a similar improvement can be achieved.
Quantum key distribution (QKD) allows two remote parties to share information-theoretically secure keys. In recent years, a revolutionary breakthrough called twin-field (TF) QKD has been developed to overcome the linear key-rate constraint and greatly increases the achievable distance. Phase randomization and subsequent postselection play roles in its security proof. Later, no-phase-postselection TF QKD was proposed and became a popular variant, since the removal of phase postselection leads to a higher key rate. However, the achievable distance is decreased compared to the original one. Here, we propose a TF QKD protocol with partial phase postselection. Namely, its code mode is still free from global phase randomization and postselection to make sure the advantage of the high key rate remain. On the other hand, phase postselection is introduced in the decoy mode to improve the performance. Applying an operator dominance condition, we prove universal security of the proposed protocol in the finite-key case under coherent attacks, and numerical simulations confirm its potential advantages in terms of key rate and achievable distance.
Quantum key distribution (QKD) could help to share a secure key between two distant peers. In recent years, twin-field (TF) QKD has been widely investigated because of its long transmission distance. One of the popular variants of TF QKD is sending-or-not-sending (SNS) QKD, which has been experimentally verified to realize 1000-km level fiber key distribution. In this article, we introduce phase postselection into the SNS protocol. With this modification, the probability of selecting ``sending'' can be substantially improved. The numerical simulation shows that the transmission distance can be improved both with and without the actively odd-parity pairing method. The case of discrete phase randomization is also analyzed, a similar improvement on distance can be seen.
Abstract Quantum key distribution (QKD) is a theoretically unconditionally secure key distribution method based on quantum mechanical principles. Currently, most QKD protocols encode information in the phase domain, making the phase error rate a crucial physical parameter for evaluating protocol performance. In phase-post-selected QKD protocols, the phase error rate depends on interference measurements within non-zero phase intervals, which introduce inherent errors unrelated to eavesdropping and consequently leads to overestimation of the phase error rate. Precise analysis of phase errors can effectively reduce the protocol’s phase error rate, thereby enhancing its performance. In previous work, phase error analysis methods were primarily applied to QKD protocols under asymptotic conditions. In this study, we extend this precise phase error analysis approach to the finite-key regime of asynchronous measurement-device-independent QKD (AMDI-QKD). The performance of the original and enhanced AMDI-QKD protocols was compared under different pulse intensities through numerical simulation, and the results indicate that, compared to the original AMDI-QKD, the enhanced AMDI-QKD protocol combined with precise error analysis can extend the transmission distance by nearly 20 km and effectively reduce the phase error rate.
In quantum cryptography, the twin-field (TF) quantum key distribution (QKD) protocol could extend theoretical key rates through a lossy channel, but most of its security proofs require phase postselection, which complicates practical systems and severely limits secure key rates. This study presents a truncated TF-QKD protocol without any postselection, gives a general security proof, and shows that this scheme may beat other protocols in terms of key rate, even when only finite decoy states are employed. By showing that a medium-range QKD system can reach much higher key rates, this protocol will make QKD systems more applicable in tomorrow's cybersecurity.