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Communications in Theoretical Physics

Performance of passive decoy-state quantum key distribution with mismatched local detectors

Kai Yu, Chunhui Zhang, Xing-Yu Zhou, Qin Wang

Published Dec 20, 2021• 1 citation
Publisher

Abstract

Abstract In quantum key distribution (QKD), the passive decoy-state method can simplify the intensity modulation and reduce some of side-channel information leakage and modulation errors. It is usually implemented with a heralded single-photon source. In Wang et al 2016 (Phys. Rev. A 96 032312), a novel passive decoy-state method is proposed by Wang et al, which uses two local detectors to generate more detection events for tightly estimating channel parameters. However, in the original scheme, the two local detectors are assumed to be identical, including the same detection efficiency and dark count rate, which is often not satisfied in the realistic experiment. In this paper, we construct a model for this passive decoy-state QKD scheme with two mismatched detectors and explore the effect on QKD performance with certain parameters. We also take the finite-size effect into consideration, showing the performance with statistical fluctuations. The results show that the efficiencies of local detectors affect the key rate more obviously than dark count rates.

DOI
10.1088/1572-9494/ac450d

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Abstract In quantum key distribution (QKD), the passive decoy-state method can simplify the intensity modulation and reduce some of side-channel information leakage and modulation errors. It is usually implemented with a heralded single-photon source. In Wang et al 2016 (Phys. Rev. A 96 032312), a novel passive decoy-state method is proposed by Wang et al, which uses two local detectors to generate more detection events for tightly estimating channel parameters. However, in the original scheme, the two local detectors are assumed to be identical, including the same detection efficiency and dark count rate, which is often not satisfied in the realistic experiment. In this paper, we construct a model for this passive decoy-state QKD scheme with two mismatched detectors and explore the effect on QKD performance with certain parameters. We also take the finite-size effect into consideration, showing the performance with statistical fluctuations. The results show that the efficiencies of local detectors affect the key rate more obviously than dark count rates.
The decoy-state method is widely used in practical quantum key distribution systems to replace ideal single photon sources with realistic light sources by varying intensities. Instead of active modulation, the passive decoy-state method employs built-in decoy states in a parametric down-conversion photon source, which can decrease the side channel information leakage in decoy state preparation and hence increase the security. By employing low dark count up-conversion single photon detectors, we have experimentally demonstrated the passive decoy-state method over a 50-km-long optical fiber and have obtained a key rate of about 100 bit/s. Our result suggests that the passive decoy-state source is a practical candidate for future quantum communication implementation.
To date, only active-decoy-state methods have been adopted in current measurement-device-independent (MDI) quantum key distribution (QKD) protocols, causing security loopholes when modulating multiple light intensities with practical devices. To solve this problem, the passive-decoy-state method will be a good choice. Until today practical passive-decoy-state MDI QKD is still missing. In this paper, based on a recently discussed structure of heralded single-photon sources, we propose a passive-decoy-state MDI QKD protocol. In present work, one does not need to modulate light sources into different intensities, but utilizes the built-in local detection events to passively generate different decoy states. Furthermore, through carrying out an appropriate mathematical method, we are able to give very precise estimations for single-photon-pair contributions. As a result, our protocol can exhibit distinct advantages compared with state-of-the-art MDI QKD schemes even when the finite-key-size effect is taken into account. Therefore, our protocol seems a promising candidate to enhance both the security and performance of MDI QKD in practical implementation.
Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. Although active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase-randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty et al., Opt. Lett. 34, 3238 (2009).] This proposal requires only linear optics together with a simple threshold photon detector, which shows the practical feasibility of the method. Most importantly, the resulting secret key rate is comparable to the one delivered by an active decoy-state setup with an infinite number of decoy settings. In this article we extend these results, now showing specifically the analysis for other practical scenarios with different light sources and photodetectors. In particular, we consider sources emitting thermal states, phase-randomized WCP, and strong coherent light in combination with several types of photodetectors, like, for instance, threshold photon detectors, photon number resolving detectors, and classical photodetectors. Our analysis includes as well the effect that detection inefficiencies and noise in the form of dark counts shown by current threshold detectors might have on the final secret key rate. Moreover, we provide estimations on the effects that statistical fluctuations due to a finite data size can have in practical implementations.
The decoy-state method could effectively enhance the performance of quantum key distribution (QKD) with a practical phase randomized weak coherent source. Although active modulation of the source intensity is effective and has been implemented in many experiments, passive preparation of decoy states is also an important addition to the family of decoy-state QKD protocols. In this paper, following the theory of Curty et al. [Phys. Rev. A 81, 022310 (2010)], we experimentally demonstrate the phase-encoding passive-decoy-state QKD with only linear optical setups and threshold single-photon detectors. In our experiment, two homemade independent pulsed lasers, with visibility of Hong-Ou-Mandel interference $0.53(\ifmmode\pm\else\textpm\fi{}0.003)$, have been implemented and used to passively generate the different decoy states. Finally, a secret key rate of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$/pulse is obtained with 10-km commercial fiber between Alice and Bob.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
The performance of active decoy-state quantum key distribution (QKD) system with a practical light source is compared with that of passive decoy-state QKD. The effect of statistical fluctuation due to a finite data size on final secret key rate is analyzed. This procedure is based on the standard error analysis on the assumption that all the variables measured in the experiment fluctuate around their asymptotic values. The relation between key generation rate and secure transmission distance is shown with exchanged quantum efficiency of threshold detector (d=1 and d=0.4) under the condition of active decoy-state (or passive decoy-state ) QKD which we pick the data size to be N=6.0109. This analysis will provide important parameters for practical QKD experiment.