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arXiv:1502.04427

A global estimation of the lower bound of the privacy amplification term for decoy-state quantum key distribution

Haodong Jiang, Ming Gao, Hong Wang, Hongxin Li, Zhi Ma

Published Feb 16, 2015• 1 citation
arXivHTMLPDF

Abstract

The privacy amplification term, of which the lower bound needs to be estimated with the decoy-state method, plays a positive role in the secure key rate formula for decoy-state quantum key distribution. In previous work, the yield and the bit error rate of single-photon state are estimated separately to gain this lower bound. In this work, we for the first time take the privacy amplification term as a whole to consider this lower bound. The mathematical description for the correlation between the yield and the bit error rate of single-photon state is given with just two unknown variables. Based on this, we obtain the global estimation of this lower bound for both BB84 protocol and measurement-device-independent protocol. The results of numerical simulation show that the global estimation can significantly improve the performance of quantum key distribution.

DOI
10.48550/arxiv.1502.04427

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The privacy amplification term, of which the lower bound needs to be estimated with the decoy-state method, plays a positive role in the secure key rate formula for decoy-state quantum key distribution. In previous work, the yield and the bit error rate of single-photon state are estimated separately to gain this lower bound. In this work, we for the first time take the privacy amplification term as a whole to consider this lower bound. The mathematical description for the correlation between the yield and the bit error rate of single-photon state is given with just two unknown variables. Based on this, we obtain the global estimation of this lower bound for both BB84 protocol and measurement-device-independent protocol. The results of numerical simulation show that the global estimation can significantly improve the performance of quantum key distribution.
The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.
We present a method without decoy state to estimate faithfully and efficiently the yield and quantum bit error rate of single photon pulse for BB84 protocol. The numerical calculations show that key generation rate and maximal secure communication distance of our method are better than results of the decoy state method. As we know, it is the first time we present this method and the idea is very novel. Furthermore, our method can overcome the drawbacks of decoy state method. In our method, the maximal secure distance is insensitive to the deviation of dark count rate from exact value.
The decoy-state method closes source security loopholes in quantum key distribution (QKD) using a laser source. In this method, accurate estimates of the detection rates of vacuum and single-photon events plus the error rate of single-photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 11%1 relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key rate of the BB84 QKD protocol with unbiased bases selection by at least 20% on average in realistic settings. The major tricks are the use of more than three types of photon intensities plus the fact that estimating bounds of the above detection and error rates is numerically stable, although these bounds are related to the inversion of a high condition number matrix.
Abstract Previous research has aimed to precisely estimate information leakage to improve the secure key rate (SKR) and maximum transmission distance in quantum key distribution (QKD). However, existing methods repeatedly considered the information of the multi-photon pulses known to Eve before and after information reconciliation, resulting in an overestimation of the leakage amount. We propose a novel approach that considers the quantum part's effect on post-processing, providing a more accurate estimation of information reconciliation leakage to improve the SKR. Theoretical analysis shows that our method more accurately estimates the information reconciliation leakage, significantly improving the SKR at any distance as well as the maximum transmission distance. It is worth mentioning that previous studies treat information leakage of the error correction as the Shannon bound Nh(e)Nh(e)Nh(e), and our method can estimate it more tightly. Simulation results for decoy-BB84 and measurement-device-independent (MDI) protocols using Cascade are consistent with the theoretical analysis. The farther the transmission distance, the greater the growth rate of SKR. When the error rate is 33%, compared with the original method, the SKR growth rate of decoy-BB84 at 100KM is 100.4%, and the transmission distance of MDI increases by 22KM.
We study the measurement-device-independent quantum key distribution (MDI-QKD) in practice with limited resources, when there are only three different states in implementing the decoy-state method. We present a tighter explicit formula to estimate the lower bound of the yield of two-single-photon pulses sent by Alice and Bob. Moreover, we show that the bounding of this yield and phase flip error of single-photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Our methods here can significantly improve the key rate and the secure distance of MDI-QKD with only three intensities.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks; thus when it is combined with the decoy-state method, the final key is unconditionally secure, even if a practical weak coherent source is used by Alice and Bob. However, until now, the analysis of decoy-state MDI-QKD with a weak coherent source is incomplete. In this paper, we derive, with only vacuum+weak decoy state, some tight formulas to estimate the lower bound of yield and the upper bound of error rate for the fraction of signals in which both Alice and Bob send a single-photon pulse to the untrusted third party Charlie. The numerical simulations show that our method with only vacuum+weak decoy state can asymptotically approach the theoretical limit of the infinite number of decoy states. Furthermore, the statistical fluctuation due to the finite length of date is also considered based on the standard statistical analysis.