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Journal of Air Force Engineering University

Statistical Fluctuation Analysis for Measurement Device Independent Quantum Key Distribution Based on the Law of Large Number

Cui Shumi

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Measurement device independent quantum key distribution is immune from all the detection attacks,so the final key is unconditional secure combined with the decoy state method.This paper analyzes statistical fluctuation analysis of finite key for the yield of single photon and quantum bit error rate of measurement-device-independent quantum key distribution by adopting the law of large number,and simulates the yield of single photon and the key rate by changing the key(N=106~1012).The result indicates that the secure transmission distance in optical fibre transmission will decrease to 260 km and 75 km respectively with the reduction of the key length,and the secure transmission distance comes to 295 km,which is close to the limitation when the key reaches to N =1012.

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Acta Physica Sinica•Jan 1, 2014•12 citations
Measurement device independent quantum key distribution is immune from all the detection attacks,so the final key is unconditional secure combined with the decoy state method.This paper analyzes statistical fluctuation analysis of finite key for the yield of single photon and quantum bit error rate of measurement-device-independent quantum key distribution by adopting the law of large number,and simulates the yield of single photon and the key rate by changing the key(N=106~1012).The result indicates that the secure transmission distance in optical fibre transmission will decrease to 260 km and 75 km respectively with the reduction of the key length,and the secure transmission distance comes to 295 km,which is close to the limitation when the key reaches to N =1012.
Measuring device-independent quantum key distribution scheme can remove all detectors' side-channel flaw, combined with decoy state program to achieve absolute security of quantum key distribution. In this paper, the statistical law of large numbers fluctuate limited key length measuring device-independent quantum key distribution scheme in single-photon counting rate and BER (Bit Error Rate) were analyzed, and the key length of the single-photon N = 106~ 1012counting rate and the key generation rate simulation were performed. Simulation results show that: in the optical fiber transmission, with decreasing key length 300km, the secure transmission distance, decreased respectively to 260km (N = 1010) and 75km (N = 106). When N = 1012, secure transmission distance is reached at 295km, close to the theoretical limit.
We present an improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with a three-intensity decoy-state method. Taking the statistical fluctuations for different sources jointly, we present more tightened formulas for some key quantities used in calculating the secure final key. Numerical simulation shows that, given the total number of pulses 1012{10}^{12}1012, our method improves the key rate by about 97% for a distance of 50 km compared with the result given by Xu et al. [F. Xu et al., Phys. Rev. A 89, 052333 (2014)], and improves the key rate by 145145%145 for a distance of 100 km compared with the result from full optimization of all parameters but treating the statistical fluctuations traditionally, i.e., treating the fluctuations for different sources separately.
Decoy state has proven to be a very useful method of significantly enhancing the performance of a quantum key distribution (QKD) system with practical light sources. The data-set size in practical QKD protocol is always finite, which will cause statistical fluctuations. The gain and the error rate of the quantum state are analyzed by considering absolutely statistical fluctuation. The relation between key generation rate and the secure communication distance is shown with exchanged quantum signal (N = 106 -1012) by the method of two-decoy-state protocol under the condition that communication wavelength is 1310 nm (or1550 nm). The result indicates that the minimal number of exchanged quantum signals increases obviously with the increase of transmission distance. The secure transmission distance is 135 km under the condition that quantum signal is 1012.
The performance of measurement-device-independent quantum key distribution (MDI-QKD) with different numbers of decoy-state are compared. The statistical fluctuation due to the finite length of data is considered based on the standard statistical analysis. The simulation results show that two-decoy-state method is a nearly optimal estimation in the asymptotic case. In the condition of considering statistical fluctuations, the finite length of raw key will slightly decrease the secret key rate. In all simulation cases, the key rate is maximized by optimizing the intensities of the signals. Our numerical simulation may provide valuable theoretical reference for the practical MDI-QKD experiments.
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.
Measurement-device-independent quantum key distribution is immune from all the detection attacks, thus when it is combined with the decoy state method, the final key is unconditional secure. In this paper, the performance of three-intensity decoy state measurement-device-independent quantum key distribution at an asymmetric channel transmittance efficiency is considered and compared with each other at the symmetric choice scenario. Simulation result shows that the key rate at the symmetric scenario can tolerate 62 dB channel loss, otherwise when the distance ratio changes, the tolerated channel loss will decrease to 37 dB and 19 dB. A method to choose the optimal intensity is proposed for asymmetric channel transmittance regardless of distance ratio, which can be easily adapted to practical experimental settings.