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Journal of Optical Technology

Secrecy of quantum key distribution with passive basis choice and detection efficiency mismatch

Egor I. Ivchenko, Anton Sergeevich Trushechkin, A. V. Khmelev, V. L. Kurochkin

Published Jul 1, 2025• 1 citation
Publisher

Abstract

Subject of study. The effect of different quantum efficiencies of single-photon detectors in quantum key distribution (QKD) systems implementing the BB84 protocol with passive basis choice is investigated. Aim of study. The aim of this study is to determine the secret key generation rate and security of the final key in quantum cryptography systems as functions of detector efficiency mismatch. Additionally, an analytical equation is derived for estimating the secret key generation rate in quantum communication systems with passive basis choice while accounting for different detector efficiencies. Method. The secret key is calculated by dividing the received measurement data according to the measurement bases, followed by performing separate post-processing for each dataset, and finally summing the resulting estimates of the secret key. Main results. An analytical method for estimating the secret key generation rate in systems with passive basis choice and mismatched detector efficiencies is developed. A satellite-to-ground quantum communication channel is modeled using the parameters of the Zvenigorod Observatory in Russia. The proposed theory for accounting for the detector efficiency mismatch is applied to a model of a satellite QKD system, and the determined length of the secret key generated during a single communication session with the satellite is found to be 300 kbit. Practical significance. The obtained results account for the effect of detector efficiency mismatch when estimating the length of the secret key in QKD systems, thereby increasing their reliability in practical implementations.

DOI
10.1364/jot.92.000468

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Subject of study. The effect of different quantum efficiencies of single-photon detectors in quantum key distribution (QKD) systems implementing the BB84 protocol with passive basis choice is investigated. Aim of study. The aim of this study is to determine the secret key generation rate and security of the final key in quantum cryptography systems as functions of detector efficiency mismatch. Additionally, an analytical equation is derived for estimating the secret key generation rate in quantum communication systems with passive basis choice while accounting for different detector efficiencies. Method. The secret key is calculated by dividing the received measurement data according to the measurement bases, followed by performing separate post-processing for each dataset, and finally summing the resulting estimates of the secret key. Main results. An analytical method for estimating the secret key generation rate in systems with passive basis choice and mismatched detector efficiencies is developed. A satellite-to-ground quantum communication channel is modeled using the parameters of the Zvenigorod Observatory in Russia. The proposed theory for accounting for the detector efficiency mismatch is applied to a model of a satellite QKD system, and the determined length of the secret key generated during a single communication session with the satellite is found to be 300 kbit. Practical significance. The obtained results account for the effect of detector efficiency mismatch when estimating the length of the secret key in QKD systems, thereby increasing their reliability in practical implementations.
Detection-efficiency mismatch is a common problem in realistic quantum key distribution (QKD) systems. The existing security proofs for the case of the passive basis choice provide a nonzero secret key rate only for a small detection-efficiency mismatch. Unfortunately, in realistic setups, the detection-efficiency mismatch can be significant. Here we present a more precise estimation of the secret key rate for the BB84 protocol with the passive basis choice, which accounts for the detection-efficiency mismatch between four threshold detectors as well as an adaptation of the decoy-state method. The suggested approach is used to estimate the secret key rate in a QKD experiment between the Micius satellite and the Zvenigorod ground station.
The decoy-state Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol is widely regarded as the de facto standard for practical implementations. On the receiver side, passive basis choice is attractive because it significantly reduces the need for random number generators and eliminates the need for optical modulators. Despite these advantages, a finite-key analytical security proof for the decoy-state BB84 protocol, where the basis is chosen passively with a biased probability, has been lacking. In this work, we present a simple analytical finite-key security proof for this setting, yielding a closed-form secret-key rate formula that can be directly evaluated using experimentally accessible parameters. Numerical simulations show that the key rates of passiveand active-measurement implementations are nearly identical, indicating that passive measurement does not compromise key-generation efficiency in practical QKD systems.
One of the challenges in practical quantum key distribution is dealing with efficiency mismatch between different threshold single-photon detectors. There are known bounds for the secret key rate for the BB84 protocol with detection-efficiency mismatch provided that the eavesdropper sends no more than one photon to the legitimate receiver. Here we improve these bounds and give tight bounds for the secret key rate with a constant detection-efficiency mismatch under the same single-photon assumption. We propose a method based on the analytical minimization of the relative entropy of coherence, which can be used in other problems in quantum key distribution. Also we propose an adaptation of the decoy state method to prove the security in the case of weak coherent pulses on the source side.
The Bennett-Brassard 1984 (BB84) protocol is one of the simplest protocols for implementing quantum key distribution (QKD). In the protocol, the sender and the receiver iteratively choose one of two complementary measurement bases. Regarding the basis choice by the receiver, a passive setup has been adopted in a number of its implementations, including satellite QKD and time-bin encoding. However, conventional theoretical techniques to prove the security of the BB84 protocol are not applicable if the receiver chooses their measurement basis passively, rather than actively, with a biased probability, followed by measurement with threshold detectors. Here we present a fully analytical security proof against coherent attacks for such a decoy-state BB84 protocol with the receiver’s passive basis choice and measurement with threshold detectors. Numerical simulations under practical situations show that the difference in secure key rate between the active and passive implementations of the protocol is negligible except for long communication distances.
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.
Quantum key distribution (QKD) protocol has been proved to provide unconditionally secure key between two remote legitimate users in theory. Key distribution signals are transmitted in a quantum channel which is established by the calibration process to meet the requirement of high count rate and low error rate. All QKD security proofs implicitly assume that the quantum channel has been established securely. However, the eavesdropper may attack the calibration process to break the security assumption of QKD and provide precondition to steal information about the final key successfully. In this paper, we reveal the security risk of the calibration process of a passive-basis-choice BB84 QKD system by launching a quantum man-in-the-middle attack which intercepts all calibration signals and resends faked ones. Large temporal bit-dependent or basis-dependent detector efficiency mismatch can be induced. Then we propose a basis-dependent detector efficiency mismatch (BEM) based faked states attack on a single photon BB84 QKD to stress the threat of BEM. Moreover, the security of single photon QKD systems with BEM is studied simply and intuitively. Two effective countermeasures are suggested to remove the general security risk of the calibration process.