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arXiv:2301.09844 · Physical Review Research

Finite-key security analysis of differential-phase-shift quantum key distribution

Akihiro Mizutani, Yuki Takeuchi, Kiyoshi Tamaki

Published May 30, 2023• 18 citations

Abstract

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.

DOI: 10.1103/physrevresearch.5.023132

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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 Differential-phase-shift (DPS) quantum key distribution stands as a promising protocol due to its simple implementation, which can be realized with a train of coherent pulses and a passive measurement unit. To implement the DPS protocol, it is crucial to establish security proofs incorporating practical imperfections in users’ devices, however, existing security proofs make unrealistic assumptions on the measurement unit using a Mach–Zehnder interferometer. In this paper, we enhance the implementation security of the DPS protocol by incorporating a major imperfection in the measurement unit. Specifically, our proof enables us to use practical beam splitters with a known range of the transmittance rather than the one with exactly 50%, as was assumed in the existing security proofs. Our numerical simulations demonstrate that even with fluctuations of ± 0.5 % in the transmittance from the ideal value, the key rate degrades only by a factor of 0.57. This result highlights the feasibility of the DPS protocol with practical measurement setups.

The performance of quantum key distribution protocols is evaluated based on the ease of implementation and key generation rate. Among major protocols, the differential-phase-shift (DPS) protocol has the advantage of simple implementation using a train of coherent pulses and a passive detection unit. Unfortunately, however, its key rate is known to be at least proportional to η 2 with respect to channel transmission η → 0 . If one can only prove the rate proportional to η 2 and cannot improve the analysis beyond that, then the DPS protocol will be deemed inferior to other major protocols, such as the decoy BB84 protocol. In this paper, we consider a type of DPS protocol in which the phase of each emitted block comprising n pulses is randomized and significantly improves the analysis of its key rate. Specifically, we reveal that the key rate is proportional to η 1 + 1 n − 2 and this scaling is tight. This implies that the DPS protocol can achieve a key rate proportional to η for a large number of n , which is the same scaling as the decoy BB84 protocol. Our result suggests that the DPS protocol can achieve a combination of both advantages of ease of implementation and a high key generation rate. Published by the American Physical Society 2024

A novel type of quantum key distribution (QKD) protocol, called DPS (differential-phase-shift) QKD, was proposed several years ago. A sender transmits a highly-attenuated coherent pulse train with {0, π} phase, and a receiver receives it with a one-bit delay Mach-Zehnder interferometer followed by photon detectors. A secret key is created from photon detection events, whose security is based on the fact that an eavesdropper cannot perfectly measure the phase information of a highly-attenuated coherent pulse train. This protocol has some features of simple setup, potential for a high key creation rate, and robustness against photon-number-splitting attack. This paper overviews DPS-QKD. The operation mechanism is described, and then some experimental efforts are introduced, featuring use of a glass waveguide Mach-Zehnder interferometer and advanced single-photon detectors. The highest key rate and the longest distance have been achieved with the DPS-QKD protocol. Some modified schemes are also presented, including that utilizing quantum entanglement, that using decoy pulses, and that using macroscopic coherent light.

Abstract To guarantee the security of quantum key distribution (QKD), security proofs of QKD protocols have assumptions on the devices. Commonly used assumptions are, for example, each random bit information chosen by a sender to be precisely encoded on an optical emitted pulse and the photon-number probability distribution of the pulse to be exactly known. These typical assumptions imposed on light sources such as the above two are rather strong and would be hard to verify in practical QKD systems. The goal of the paper is to replace those strong assumptions on the light sources with weaker ones. In this paper, we adopt the differential-phase-shift (DPS) QKD protocol and drastically mitigate the requirements on light sources, while for the measurement unit, trusted and photon-number-resolving detectors are assumed. Specifically, we only assume the independence among emitted pulses, the independence of the vacuum emission probability from a chosen bit, and upper bounds on the tail distribution function of the total photon number in a single block of pulses for single, two and three photons. Remarkably, no other detailed characterizations, such as the amount of phase modulation, are required. Our security proof significantly relaxes demands for light sources, which paves a route to guarantee implementation security with simple verification of the devices.

We demonstrate the first proof of principle differential phase shift (DPS) quantum key distribution (QKD) using narrow-band heralded single photons with amplitude-phase modulations. In the 3-pulse case, we obtain a quantum bit error rate (QBER) as low as 3.06% which meets the unconditional security requirement. As we increase the pulse number up to 15, the key creation efficiency approaches 93.4%, but with a cost of increasing the QBER. Our result suggests that narrow-band single photons maybe a promising source for the DPS-QKD protocol.