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IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC)

Analysis for device independent quantum key distribution based on the law of large number

Na Li, Shumin Cui, Yi-Mmg Ji, Kui-sheng Feng, Lei Shi

Published Dec 1, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iaeac.2015.7428723

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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.
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.
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.
How to remove detector side channel attacks has been a notoriously hard problem in quantum cryptography. Here, we propose a simple solution to this problem--measurement-device-independent quantum key distribution (QKD). It not only removes all detector side channels, but also doubles the secure distance with conventional lasers. Our proposal can be implemented with standard optical components with low detection efficiency and highly lossy channels. In contrast to the previous solution of full device independent QKD, the realization of our idea does not require detectors of near unity detection efficiency in combination with a qubit amplifier (based on teleportation) or a quantum nondemolition measurement of the number of photons in a pulse. Furthermore, its key generation rate is many orders of magnitude higher than that based on full device independent QKD. The results show that long-distance quantum cryptography over say 200 km will remain secure even with seriously flawed detectors.
A measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to all detection side-channel attacks and guarantees the information-theoretical security even with uncharacterized single photon detectors. A weak coherent source is used in the current MDI-QKD experiments, it inevitably contains a certain percentage of vacuum and multi-photon pulses. The security issues introduced by these source imperfections can be avoided by applying the decoy state method. Here, through modeling experimental devices, and taking into account the weak coherent source and the threshold detectors, we have evaluated the gain, the probability to get successful Bell measurement and incorrect Bell measurement, and the quantum bit error rate (QBER), given a practical setup. In our simulation, we show how QBER varies with different transmission distances in the cases when the average photon numbers per pulse from Alice and Bob are symmetric and asymmetric. Result shows that the multi-photon pulses do not cause error in the Z basis of polarization encoding scheme, but produce a large QBER in phase encoding scheme and in the X basis of polarization encoding scheme. QBER is affected by the dark count rate and the system optical error associated with the multi-photon pulses. For different encoding schemes, QBER caused by each kind of average photon numbers from Alice and Bob increases to different degrees with the transmission distance, and finally is close to 50%. With the increase of the transmission distance, the average photon number per pulse decreases and the fraction of the dark count rate causing QBER gradually increases. Under the same effect of the dark count rate, the smaller the average photon number per pulse, the bigger the QBER. After a certain transmission and at the same transmission distance, the QBER is largest when average photon numbers used by Alice and Bob are both smallest. For the short distance transmission of phase encoding scheme and the X basis, we find that QBER is larger when average photon numbers from the two arms are asymmetric, as compared to the symmetric case. For the Z basis, the QBER caused by the system optical error and the dark count rate is very small.
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.
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.