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Acta Physica Sinica

Analysis on quantum bit error rate in measurement-device-independent quantum key distribution using weak coherent states

Yanan Du, Xie Wen-Zhong, Jin Xuan, Jindong Wang, Zhengjun Wei, Qin Xiao-Juan, Zhao Feng, Zhi‐Ming Zhang

Published Jan 1, 2015• 6 citations
Publisher

Abstract

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.

DOI
10.7498/aps.64.110301

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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.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all detection side-channel attacks, thus when combined with the decoy-state method, it can avoid the actual security loophole caused by quasisingle- photon source simultaneously. A practical weak coherent source is used as a quasi-single-photon source in the current MDI-QKD experiments; it may contain percentage of vacuum-and multi-photon pulses. Moreover, in order to study how the performance of the threshold detector affects the quantum bit error rate (QBER), we introduce the quality factor (the ratio of the dark count rate to the detection efficiency) of the threshold detector. Here, through taking into account the weak coherent source, the quality factor of the threshold detector and the reflectivity of beam splitter, we deduce and evaluate the gain, the probability for successful Bell measurement, incorrect Bell measurement when Alice and Bob send pulses with different photon numbers which have a high probability to appear in weak coherent source, and then we obtain QBER in combination with the probabilities of different photon number states, besides, we also do some simulations. The simulations show how QBER varies with the reflectivity of beam splitter and the quality factor of the threshold detector when the average photon numbers per pulse from Alice and Bob are symmetric. Furthermore, the simulations show how QBER varies with the average photon number per pulse from Alice when average photon number per pulse from Bob is 0.1. Result shows that QBER is affected by the reflectivity of beam splitter, but QBER cannot reach the minimum value in Z basis encoding scheme when the average photon numbers per pulse from Alice and Bob are both 0.1 and the reflectivity of beam splitter is 0.5, which is different from X basis encoding and phase encoding. In addition, QBER increases with the increase of the quality factor of the threshold detector, which means that better performance of the threshold detector will reduce QBER. We show that QBER in Z basis encoding reaches the minimum value when reflectivity of beam splitter is 0.5 and there is large difference between in average photon number per pulse between two sides. In conclusion, for QBER, the effect from the reflectivity of beam splitter is equal to average photon numbers from the two arms only in X basis encoding and phase encoding. Our work will provide a reference for setting up a system with better performance.
The ideal measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is built on the Bell state measurement of two single-photon states. However, in practical MDI-QKD where phase-randomized weak coherent pulses (PR-WCPs) are used, the mismatch between states preparation and measurement in X basis leads to the bit error rate of more than 25%, which poses a challenge to the security of QKD. In this paper, we provide a security analysis of practical MDI-QKD based on polarization coding. We analyze the Hong-Ou-Mandel interference of PR-WCPs and Poisson-distributed photon number states (PNs), and find that these two sources are equivalent in MDI-QKD. The security analysis based on entanglement distillation is carried out on PNs, and the measurement results in Z basis and X basis are averaged to overcome the noncorrelation of the error rates in these two bases. Compared with GLLP scheme, a tighter key rate is obtained in this work, and the key rate deviates from the linear key rate bound in a short distance due to the finite proportion of multiphoton terms.
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 rate can be obtained by estimating the gain and quantum bit error rate for various input photon numbers. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy-state MDI-QKD with OCS and obtain a practical key rate.
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.
Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) is a two-photon protocol devised to eliminate eavesdropping attacks that interrogate or control the detector in realized quantum key distribution systems. In MDI-QKD, the measurements are carried out by an untrusted third party, and the measurement results are announced openly. Knowledge or control of the measurement results gives the third party no information about the secret key. Error-free implementation of the MDI-QKD protocol requires the crypto-communicating parties, Alice and Bob, to independently prepare and transmit single photons that are physically indistinguishable, with the possible exception of their polarization states. In this paper, we apply the formalism of quantum optics and Monte Carlo simulations to quantify the impact of small errors in wavelength, bandwidth, polarization and timing between Alice's photons and Bob's photons on the MDI-QKD quantum bit error rate (QBER). Using published single-photon source characteristics from two-photon interference experiments as a test case, our simulations predict that the finite tolerances of these sources contribute (4.04+/-20/Nsifted) to the QBER in an MDI-QKD implementation generating an Nsifted-bit sifted key.
Measurement-device-independent quantum key distribution (MDI-QKD) can be immune to all detector side-channel attacks and guarantee the information-theoretical security even with uncharacterized single photon detectors. MDI-QKD has been demonstrated in both laboratories and field-tests by using attenuated lasers combined with the decoy-state technique. However, it is a critical assumption that the sources used by legitimate participants are trusted in MDI-QKD. Hence, it is possible that a potential security risk exists. Here we propose a new scheme of polarization-encoding-based MDI-QKD with a single untrusted source, by which the complexity of the synchronization system can be reduced and the success rate of the Bell-state measurement can be improved. Meanwhile, the decoy-state method is employed to avoid the security issues introduced by a non-ideal single photon source. We also derive a security analysis of the proposed system. In addition, it seems to be a promising candidate for the implementation for QKD network in the near future.