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arXiv:0811.2628 · New Journal of Physics

Finite-key analysis for practical implementations of quantum key distribution

Raymond Y Q Cai, Valerio Scarani

Published Apr 1, 2009• 167 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/11/4/045024

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We present a tight security analysis of the Bennett–Brassard 1984 protocol taking into account the finite-size effect of key distillation and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Next we show that a similar tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their quantum key distribution systems, we also give the explicit procedures of our key distillation and show how to calculate the secret key rate and the security parameter from a given set of experimental parameters. In addition to the exact values of key rates and security parameters, we also describe how to obtain their rough estimates using the normal approximation.
The length of signal pulses is finite in practical quantum key distribution. The finite-key analysis of an unconditional quantum key distribution is a burning problem, and the efficient quantum key distribution protocol suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD), was proposed very recently. We give the finite-key analysis of MDI QKD, which removes all detector side channels and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The secure bound of the ultimate key rate is obtained under the statistical fluctuations of relative frequency, which can be applied directly to practical threshold detectors with low detection efficiency and highly lossy channels. The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure distance is around 10 km when the number of sifted data is 1010{10}^{10}1010. Moreover the secure distance would be much longer in practice because of some simplified treatments used in our paper.
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.
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.