Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2201.03039 · Entropy

Finite-Key Analysis for Quantum Key Distribution with Discrete-Phase Randomization

Rui-Qiang Wang, Zhen−Qiang Yin, Xiao-Hang Jin, Rong Wang, Shuang Wang, Wei Chen, Guang‐Can Guo, Zheng‐Fu Han

Published Jan 31, 2023• 5 citations
arXivHTMLPDF

Abstract

Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2π, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,π/4,π/2,…,7π/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.

DOI
10.3390/e25020258

Related papers

Security of advanced quantum key distribution protocols in realistic conditions

Currás Lorenzo, José Guillermo

Quantum key distribution (QKD) allows two users to generate a random secret key, which they can use to securely exchange a message. Unlike many other cryptographic schemes, QKD offers information-theoretical security based on the laws of physics. In recent years, major theoretical and experimental advancements have been made. Among these are two novel protocols, memory-assisted (MA) QKD and twin-field (TF) QKD, which can both improve the secret-key rate scaling with channel length, potentially allowing QKD to be performed at longer distances. The main motivation of this thesis is to incorporate more realistic assumptions into the security proofs and performance analyses of these new protocols. \n \n \nOne common assumption made in QKD security proofs is that the protocol is run for an infinitely long time, which allows the users to obtain a perfect statistical characterisation of the quantum channel. In this thesis, we drop this assumption for a TF-QKD variant that is well suited for experimental implementation, proving its security in the finite-key regime. We also analyse the finite-key performance of MA-QKD, concluding that it is particularly resistant to its statistical fluctuation effects. Moreover, we develop an alternative finite-key security analysis approach based on random sampling theory, and apply it to the loss-tolerant protocol, which can ensure security in the presence of flawed sources. Compared to previous finite-key security proofs of the protocol, our analysis offers better performance. \n \n \nAnother common assumption is that the users can emit laser pulses with a continuous random phase. In practice, this is difficult to achieve, and the phase is often randomised discretely. In this thesis, we prove the security of a TF-QKD variant that relies on discrete phase randomisation, and show that, using certain post-selection techniques, it can provide higher secret-key rates than an equivalent continuously-randomised protocol.

•May 1, 2021•0 citations

Twin-Field Quantum Key Distribution with Discrete-Phase-Randomized Sources

Chun-Mei Zhang, Yiwei Xu, Rong Wang +1 more

Due to the single-photon interference at a third untrusted party, the twin-field quantum key distribution (TF-QKD) protocol and its variants can beat the well-known rate-loss bound without quantum repeaters and related experiments have recently been implemented. In general, quantum states in these schemes should be randomly switched between the code mode and the test mode. To adopt the standard decoy-state method, the phases of coherent-state sources in the test mode are assumed to be continuously randomized. However, such a crucial assumption cannot be satisfied well in experimental implementations. In this paper, to bridge the gap between theory and practice, we propose a TF-QKD variant with discrete-phase-randomized sources both in the code mode and the test mode and prove its security against collective attacks. Our simulation results indicate that, with only a small number of discrete phases, the performance of discrete-phase-randomized sources can overcome the rate-loss bound and approach that of continuous-phase-randomized sources.

arXiv:2008.05277•Physical Review Applied•Dec 24, 2020•16 citations

Discrete-phase-randomized twin-field quantum key distribution with advantage distillation

Chun-Mei Zhang, Zhe Wang, Yu-Da Wu +3 more

The twin-field quantum key distribution (TF-QKD) protocol and its variants provide promising solutions to long-distance information-theoretic-secure communication, which can surpass the fundamental rate-loss bound without quantum repeaters. Different from other variants, the discrete-phase-randomized TF-QKD variant only needs to modulate weak coherent sources with random discrete phases, which avoids the necessity of modulating continuously randomized phases and can be implemented with current technology. However, the discrete-phase-randomized variant compromises the performance of TF-QKD under high channel losses and error rates. To overcome this dilemma, we propose to adopt the advantage distillation method to improve the performance of discrete-phase-randomized TF-QKD, and analyze its security in the asymptotic case. Without changing the optical hardware of TF-QKD systems, the proposed scheme can improve the secret key rate under high channel losses and error rates, and extend the tolerable channel loss as well.

Physical Review A•May 22, 2024•11 citations

Twin-Field Quantum Key Distribution with Partial Phase Postselection

Yao Zhou, Zhen−Qiang Yin, Rui-Qiang Wang +4 more

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.

arXiv:2211.12688•Physical Review Applied•Nov 9, 2022•9 citations

Optimized protocol for twin-field quantum key distribution

Rong Wang, Zhen-Qiang Yin, Feng-Yu Lu +7 more

Abstract Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.

arXiv:1904.07074•Communications Physics•Aug 28, 2020•41 citations

Finite key analysis for discrete phase randomized BB84 protocol

Xiao-Hang Jin, Zhen−Qiang Yin, Shuang Wang +3 more

Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.

Quantum Information Processing•Aug 31, 2024•2 citations
Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2π, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,π/4,π/2,…,7π/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.
Quantum key distribution (QKD) allows two users to generate a random secret key, which they can use to securely exchange a message. Unlike many other cryptographic schemes, QKD offers information-theoretical security based on the laws of physics. In recent years, major theoretical and experimental advancements have been made. Among these are two novel protocols, memory-assisted (MA) QKD and twin-field (TF) QKD, which can both improve the secret-key rate scaling with channel length, potentially allowing QKD to be performed at longer distances. The main motivation of this thesis is to incorporate more realistic assumptions into the security proofs and performance analyses of these new protocols. \n \n \nOne common assumption made in QKD security proofs is that the protocol is run for an infinitely long time, which allows the users to obtain a perfect statistical characterisation of the quantum channel. In this thesis, we drop this assumption for a TF-QKD variant that is well suited for experimental implementation, proving its security in the finite-key regime. We also analyse the finite-key performance of MA-QKD, concluding that it is particularly resistant to its statistical fluctuation effects. Moreover, we develop an alternative finite-key security analysis approach based on random sampling theory, and apply it to the loss-tolerant protocol, which can ensure security in the presence of flawed sources. Compared to previous finite-key security proofs of the protocol, our analysis offers better performance. \n \n \nAnother common assumption is that the users can emit laser pulses with a continuous random phase. In practice, this is difficult to achieve, and the phase is often randomised discretely. In this thesis, we prove the security of a TF-QKD variant that relies on discrete phase randomisation, and show that, using certain post-selection techniques, it can provide higher secret-key rates than an equivalent continuously-randomised protocol.
Due to the single-photon interference at a third untrusted party, the twin-field quantum key distribution (TF-QKD) protocol and its variants can beat the well-known rate-loss bound without quantum repeaters and related experiments have recently been implemented. In general, quantum states in these schemes should be randomly switched between the code mode and the test mode. To adopt the standard decoy-state method, the phases of coherent-state sources in the test mode are assumed to be continuously randomized. However, such a crucial assumption cannot be satisfied well in experimental implementations. In this paper, to bridge the gap between theory and practice, we propose a TF-QKD variant with discrete-phase-randomized sources both in the code mode and the test mode and prove its security against collective attacks. Our simulation results indicate that, with only a small number of discrete phases, the performance of discrete-phase-randomized sources can overcome the rate-loss bound and approach that of continuous-phase-randomized sources.
The twin-field quantum key distribution (TF-QKD) protocol and its variants provide promising solutions to long-distance information-theoretic-secure communication, which can surpass the fundamental rate-loss bound without quantum repeaters. Different from other variants, the discrete-phase-randomized TF-QKD variant only needs to modulate weak coherent sources with random discrete phases, which avoids the necessity of modulating continuously randomized phases and can be implemented with current technology. However, the discrete-phase-randomized variant compromises the performance of TF-QKD under high channel losses and error rates. To overcome this dilemma, we propose to adopt the advantage distillation method to improve the performance of discrete-phase-randomized TF-QKD, and analyze its security in the asymptotic case. Without changing the optical hardware of TF-QKD systems, the proposed scheme can improve the secret key rate under high channel losses and error rates, and extend the tolerable channel loss as well.
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.
Abstract Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.
Abstract Quantum key distribution (QKD) is a secure communication method that relies on the inherent randomness of quantum mechanics to ensure information-theoretic security. The first and most widely used QKD protocol is BB84, and the proof of BB84's security is vital. The Discrete Phase Randomized BB84 protocol is a variant of the decoy BB84 protocol. It has been proven to be promising in the development of high-speed QKD systems. However, it still lacks an analysis with a finite number of pulses. This paper presents a comprehensive security analysis of the discrete phase BB84 protocol, using two different methods under different conditions. The analysis involves simulations and optimizations to determine the optimal parameter settings. It is confirmed that for typical scenarios, if the number of discrete phases exceeds 30, one can calculate the key rate by assuming that a continuous phase randomization process was in operation. On the other hand, for a relatively smaller number of discrete values, we have developed a numerical method to calculate the key rate. We have confirmed that its performance is reduced but still acceptable with a finite number of pulses.