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

TL;DR

This paper improves the finite-key security analysis of the differential-phase-shift quantum key distribution protocol by using Kato's inequality, significantly increasing the achievable key rate in practical scenarios.

Contribution

It introduces the application of Kato's inequality to finite-size security analysis of DPS QKD, overcoming limitations of Azuma's inequality and enhancing key rate performance.

Findings

Key rate is drastically improved using Kato's inequality.

A 3 Mbit secret key can be generated over 77 km in 8.3 hours.

Demonstrates feasibility of DPS QKD with realistic parameters.

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 has been established in [npj Quant. Inf. 5, 87 (2019)] assuming the 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.