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arXiv:2301.11340 · Quantum

Security of differential phase shift QKD from relativistic principles

Martin Sandfuchs, Michael Haberland, V. Vilasini, Ramona Wolf

Published Jan 27, 2025• 15 citations

Abstract

The design of quantum protocols for secure key generation poses many challenges: On the one hand, they need to be practical concerning experimental realisations. On the other hand, their theoretical description must be simple enough to allow for a security proof against all possible attacks. Often, these two requirements are in conflict with each other, and the differential phase shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be implementable with current optical telecommunication technology, which, for this protocol, comes at the cost that many standard security proof techniques do not apply to it. After about 20 years since its invention, this work presents the first full security proof of DPS QKD against general attacks, including finite-size effects. The proof combines techniques from quantum information theory, quantum optics, and relativity. We first give a security proof of a QKD protocol whose security stems from relativistic constraints. We then show that security of DPS QKD can be reduced to security of the relativistic protocol. In addition, we show that coherent attacks on the DPS protocol are, in fact, stronger than collective attacks. Our results have broad implications for the development of secure and reliable quantum communication technologies, as they shed light on the range of applicability of state-of-the-art security proof techniques.

DOI: 10.22331/q-2025-01-27-1611

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The design of quantum protocols for secure key generation poses many challenges: On the one hand, they need to be practical concerning experimental realisations. On the other hand, their theoretical description must be simple enough to allow for a security proof against all possible attacks. Often, these two requirements are in conflict with each other, and the differential phase shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be implementable with current optical telecommunication technology, which, for this protocol, comes at the cost that many standard security proof techniques do not apply to it. After about 20 years since its invention, this work presents the first full security proof of DPS QKD against general attacks, including finite-size effects. The proof combines techniques from quantum information theory, quantum optics, and relativity. We first give a security proof of a QKD protocol whose security stems from relativistic constraints. We then show that security of DPS QKD can be reduced to security of the relativistic protocol. In addition, we show that coherent attacks on the DPS protocol are, in fact, stronger than collective attacks. Our results have broad implications for the development of secure and reliable quantum communication technologies, as they shed light on the range of applicability of state-of-the-art security proof techniques.

Differential-phase-shift (DPS) quantum key distribution (QKD) is one of the major QKD protocols that can be implemented with a simple setup using a laser source and a passive detection unit. Recently, an information-theoretic security proof of this protocol was established by Mizutani et al. [npj Quantum Inf. 5, 87 (2019)], assuming an infinitely large number of emitted pulses. To implement the DPS protocol in a real-life world, it is indispensable to analyze the security with the finite number of emitted pulses. The extension of the security proof to the finite-size regime requires the accommodation of the statistical fluctuations to determine the amount of privacy amplification. In doing so, Azuma's inequality is often employed, but unfortunately we show that in the case of the DPS protocol, this results in a substantially low key rate. This low key rate is due to a loose estimation of the sum of probabilities regarding three-photon emission whose probability of occurrence is very small. The main contribution of our work is to show that this obstacle can be overcome by exploiting the recently found novel concentration inequality, Kato's inequality. As a result, the key rate of the DPS protocol is drastically improved. For instance, assuming typical experimental parameters, a 3-Mbit secret key can be generated over 77 km for 8.3 hours, which shows the feasibility of DPS QKD under a realistic setup.

Abstract We prove the information-theoretic security of the differential-phase-shift (DPS) quantum key distribution (QKD) protocol in the asymptotic regime based on the complementarity approach (arXiv:0704.3661 (2007)). Our security proof provides a slightly better key generation rate compared to the one derived in the previous security proof in (arXiv:1208.1995 (2012)) that is based on the Shor–Preskill approach (Shor and Preskill 2000 Phys. Rev. Lett. 85 441). This improvement is obtained because the complementarity approach can employ more detailed information on Alice’s sending state in estimating the leaked information to an eavesdropper. Moreover, we remove the necessity of the numerical calculation that was needed in the previous analysis to estimate the leaked information. This leads to an advantage that our security proof enables us to evaluate the security of the DPS protocol with any block size. This paper highlights one of the fundamental differences between the Shor–Preskill and the complementarity approaches.

In this Letter, we prove the unconditional security of the single-photon differential phase shift quantum key distribution (DPS-QKD) protocol, based on the conversion to an equivalent entanglement-based protocol. We estimate the upper bound of the phase error rate from the bit error rate, and show that the DPS-QKD protocol can generate an unconditionally secure key when the bit error rate is not greater than 4.12%. This proof is the first step to the unconditional security proof of a coherent state DPS-QKD.

ABSTRACT This paper analyzes the information‐theoretical security of the of Differential Phase Shift (DPS) Quantum Key Distribution (QKD) protocol, using efficient computational information geometric algorithms. The protocol was introduced for practical reasons, since the earlier QKD schemes were too complicated to implement in practice. The DPS QKD protocol can be an integrated part of current network security applications; hence its practical implementation is much easier with the current optical devices and optical networks. The proposed algorithm could be a very valuable tool to answer the still open questions related to the security bounds of the DPS QKD protocol. Copyright © 2012 John Wiley & Sons, Ltd.

Differential phase shift keying constitutes a pathway towards practical quantum key distribution by using affordable commercial technologies, and robust theoretical foundations. Recent advances have proven its security against general adversaries, albeit requiring limitations, including strong repetition rate constraints at the security proof and costly statistical estimators. In this work, we overcome said limitations by considering an alternative scheme, herewith denominated relativistic phase shift keying (RPSK). We leverage variable-length general security techniques via entropy accumulation, together with methods based on Rényi leftover hashing and conic optimization. Our approach achieves secret key rates with

10^5

signals beyond 12 dB, constituting a robust proof of the experimental implementability of RPSK.