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arXiv:1210.3929 · Physical Review A

Statistical fluctuation analysis for measurement-device-independent quantum key distribution

Xiongfeng Ma, Chi‐Hang Fred Fung, Mohsen Razavi

Published Nov 5, 2012• 190 citations
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Abstract

Measurement-device-independent quantum key distribution with a finite number of decoy states is analyzed under finite-data-size assumption. By accounting for statistical fluctuations in parameter estimation, we investigate vacuum+weak- and vacuum+two-weak-decoy-state protocols. In each case, we find proper operation regimes, where the performance of our system is comparable to the asymptotic case for which the key size and the number of decoy states approach infinity. Our results show that practical implementations of this scheme can be both secure and efficient.

DOI
10.1103/physreva.86.052305

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Measurement-device-independent quantum key distribution with a finite number of decoy states is analyzed under finite-data-size assumption. By accounting for statistical fluctuations in parameter estimation, we investigate vacuum+weak- and vacuum+two-weak-decoy-state protocols. In each case, we find proper operation regimes, where the performance of our system is comparable to the asymptotic case for which the key size and the number of decoy states approach infinity. Our results show that practical implementations of this scheme can be both secure and efficient.
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.
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.
Every security analysis of quantum key distribution relies on a faithful modeling of the employed quantum states. The properties of decoy state protocol based on only two decoy states and one signal state are analyzed. The performance of decoy state quantum key distribution protocol with finite resources is calculated by considering the statistical fluctuation for the yield and error rate of the quantum state. The relationship between key generation rate and transmission distance is compared by considering the data-set size to be N=108 (N=109 or N=1010 or the asymptotic case). These may provide some important parameters for the practical quantum key distribution system.
In this paper, we consider the decoy-state Measurement-Device-Independent Quantum key distribution (MDI-QKD) with four intensities. The average value of successful events and bit errors among the pulse pair set be used to investigate the successful events of different pulses under the statistical fluctuation caused by the finite condition. We demonstrate that the lower bound of successful events number n11estimated by our method can be more tight than the result in [28]. Numerical simulations show that our estimation method can achieve a higher key rate than existing methods with a relatively weak constraints of experimental devices, such as high dark count rate and low detection efficiency of detectors when data size is N = 109.
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Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol that eliminates all possible attacks on the detector side and the necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations since more parameters, e.g., yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy states method estimates these yields overpessimistically since it ignores the potential relations between different bases. Through jointly processing parameters of different bases, the performance of RFI-MDI-QKD is greatly improved in terms of the secret key rate and achievable distance when statistical fluctuations are considered (the statistical fluctuation analysis is the first step to the final analysis of the finite key size effect). Our results pave an avenue towards practical RFI-MDI-QKD.