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 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.
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.
A novel protocol, measurement-device-independent quantum key distribution (MDI-QKD), removes all attacks from the detection system, the most vulnerable part in QKD implementations. In this paper, we present an analysis for practical aspects of MDI-QKD. To evaluate its performance, we study various error sources by developing a general system model. We find that MDI-QKD is highly practical and thus can be easily implemented with standard optical devices. Moreover, we present a simple analytical method with only two (general) decoy states for the finite decoy-state analysis. This method can be used directly by experimentalists to demonstrate MDI-QKD. By combining the system model with the finite decoy-state method, we present a general framework for the optimal choice of the intensities of the signal and decoy states. Furthermore, we consider a common situation, namely asymmetric MDI-QKD, in which the two quantum channels have different transmittances. We investigate its properties and discuss how to optimize its performance. Our work is of interest not only to experiments demonstrating MDI-QKD but also to other non-QKD experiments involving quantum interference.
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.
Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual performance of former demonstrations. Here, we present analytical and numerical decoy-state methods with one, two, and three decoy states. We provide a clear comparison among these methods and find that two decoy states already enable a near-optimal estimation and more decoy states cannot improve the key rate much in either asymptotic or finite-data settings. Furthermore, we perform a full optimization of system parameters and show that full optimization can significantly improve the key rate in the finite-data setting. By simulating a real experiment, we find that full optimization can increase the key rate by more than one order of magnitude compared to nonoptimization. A local search method to optimize efficiently the system parameters is proposed. This method can be four orders of magnitude faster than a trivial exhaustive search to achieve a similar optimal key rate. We expect that this local search method could be valuable for general fields in physics.
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detector loopholes. When it is combined with the decoy-state method, the final key is unconditionally secure, even if Alice and Bob do not have strict single-photon sources. However, active modulation of source intensity, which is used to generate the decoy state, may leave side channels and leak additional information to Eve. In this paper, we consider the MDI-QKD with a passive decoy state, in which both Alice and Bob send pulses to an untrusted third party, Charlie. Then, in order to estimate the key generation rate, we derive two tight formulas to estimate the lower bound of the yield and the upper bound of the error rate that both Alice and Bob send a single-photon pulse to Charlie. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the standard statistical analysis.