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arXiv:2511.21253 · Quantum Science and Technology

Finite-key security analysis of the decoy-state BB84 QKD with passive measurement

Akihiro Mizutani, Shun Kawakami, Go Kato

quant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025• 2 citations
arXivHTMLPDF

Abstract

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.

Journal reference
Quantum Science and Technology 11, 015010 (2025)
DOI
10.1088/2058-9565/ae20b9
Comments
21 pages, 3 figures

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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.
The passive approach to quantum key distribution (QKD) eliminates all optical modulators and random number generators from QKD systems reaching an enhanced simplicity, immunity to modulator side channels, and potentially higher repetition rates. In this work, we provide finite-key security bounds for a fully passive decoy-state Bennett-Brassard 1984 (BB84) protocol, considering a recently presented passive QKD source. With our analysis, the attainable secret-key rate is comparable to that of the perfect parameter-estimation limit, in fact differing from the key rate of the active approach by less than one order of magnitude. This demonstrates the practicality of fully passive QKD solutions.
Entanglement-based key distribution protocols, such as the Bennett-Brassard-Mermin 1992 (BBM92) protocol and quantum conference key agreement (QCKA), are promising applications of quantum networks. In practical implementations, passive measurement setups are widely adopted because of their simplicity. However, the security analysis of passive protocols with biased basis choice is highly nontrivial, since standard proof techniques for threshold detectors are generally not applicable in this setting. In this work, we establish the security of passive entanglement-based key distribution protocols in the asymptotic regime. Specifically, we prove the security of passive BBM92 with biased basis choice and extend the proof to passive QCKA with an arbitrary number of parties. In addition, we numerically show that the key generation rate of passive BBM92 is almost identical to that of the corresponding active protocol. Our results provide a theoretical foundation for practical passive implementations of entanglement-based key distribution protocols.
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.
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.
Security proofs of quantum key distribution (QKD) typically assume that the devices of the legitimate users are perfectly shielded from the eavesdropper. This assumption is, however, very hard to meet in practice, and thus the security of current QKD implementations is not guaranteed. Here, we fill this gap by providing a finite-key security analysis for QKD which is valid against arbitrary information leakage from the state preparation process of the legitimate users. For this, we extend the techniques introduced by Tamaki et al (2016 New J. Phys. 18 065008) to the finite-key regime, and we evaluate the security of a leaky decoy-state BB84 protocol with biased basis choice, which is one of the most implemented QKD schemes today. Our simulation results demonstrate the practicability of QKD over long distances and within a reasonable time frame given that the legitimate users' devices are sufficiently isolated.
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and most importantly, the security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is the deviation between phase error rate of computational basis and bit error rate of dual basis. Here, we provide the rigorous and optimal analytic formula to solve the above tasks, resulting to higher secret key rate and longer secure transmission distance. Our results can be widely applied to deal with statistical fluctuation in quantum cryptography protocols.