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Quantum Information and Computation

Finite-key analysis for quantum key distribution with decoy states

Tingting Song, Jie Zhang, Su‐Juan Qin, Fei Gao, Qiaoyan Wen

Published May 1, 2011• 9 citations
Publisher

Abstract

We analyze the security of finite-resource quantum key distribution with decoy states, and present the security bound for the practical implementations by introducing the deviations of the probability of sending a $k$-photon pulse and the error rate of the quantum state. The bound is simulated under reasonable values of the observed parameters. Compared with the previous works, the security bound is more stringent.

DOI
10.26421/qic11.5-6-2

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We analyze the security of finite-resource quantum key distribution with decoy states, and present the security bound for the practical implementations by introducing the deviations of the probability of sending a kkk-photon pulse and the error rate of the quantum state. The bound is simulated under reasonable values of the observed parameters. Compared with the previous works, the security bound is more stringent.
Abstract Compared with two-level quantum key distribution (QKD), high-dimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finite-key security analysis for the recently proposed practical high-dimensional decoy-state QKD protocol based on time-energy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the secure-key capacity. By numerical evaluation, we show the finite-key effect on the secure-key capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of high-dimensional QKD.
The quantum key distribution (QKD) allows two parties to share a secret key by typically making use of a one-way quantum channel. However, the two-way QKD has its own unique advantages, which means the two-way QKD has become a focus recently. To improve the practical performance of the two-way QKD, we present a security analysis of a two-way QKD protocol based on the decoy method with heralded single-photon sources (HSPSs). We make use of two approaches to calculate the yield and the quantum bit error rate of single-photon and two-photon pulses. Then we present the secret key generation rate based on the GLLP formula. The numerical simulation shows that the protocol with HSPSs has an advantage in the secure distance compared with weak coherent state sources. In addition, we present the final secret key generation rate of the LM05 protocol with finite resources by considering the statistical fluctuation of the yield and the error rate.
Every security analysis of quantum key distribution relies on a faithful modeling of the employed quantum states. The properties of decoy state protocol based on only two decoy states and one signal state are analyzed. The performance of decoy state quantum key distribution protocol with finite resources is calculated by considering the statistical fluctuation for the yield and error rate of the quantum state. The relationship between key generation rate and transmission distance is compared by considering the data-set size to be N=108 (N=109 or N=1010 or the asymptotic case). These may provide some important parameters for the practical quantum key distribution system.
The lists of bits processed in quantum key distribution are necessarily of finite length. The need for finite-key unconditional security bounds was recognized long ago, but the theoretical tools have become available only very recently. We provide finite-key unconditional security bounds for two practical implementations of the Bennett–Brassard 1984 coding: prepare-and-measure implementations without decoy states and entanglement-based implementations. A finite-key bound for prepare-and-measure implementations with decoy states is also derived under a simplified treatment of the statistical fluctuations. The presentation is tailored to allow direct application of the bounds in experiments. Finally, the bounds are also evaluated on a priori reasonable expected values of the observed parameters.