Decoy-state Method Research Articles

Measurement-device-independent quantum key distribution with a passive decoy-state method

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.

Long-distance measurement-device-independent quantum key distribution with coherent-state superpositions.

Measurement-device-independent quantum key distribution (MDI-QKD) with decoy-state method is believed to be securely applied to defeat various hacking attacks in practical quantum key distribution systems. Recently, the coherent-state superpositions (CSS) have emerged as an alternative to single-photon qubits for quantum information processing and metrology. Here, in this Letter, CSS are exploited as the source in MDI-QKD. We present an analytical method that gives two tight formulas to estimate the lower bound of yield and the upper bound of bit error rate. We exploit the standard statistical analysis and Chernoff bound to perform the parameter estimation. Chernoff bound can provide good bounds in the long-distance MDI-QKD. Our results show that with CSS, both the security transmission distance and secure key rate are significantly improved compared with those of the weak coherent states in the finite-data case.

Analysis of measurement-device-independent quantum key distribution under asymmetric channel transmittance efficiency

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks. Based on decoy-state method, MDI-QKD can be implemented with nonperfect single-photon sources. In this paper, the performance of three-intensity decoy-state MDI-QKD under asymmetric channel transmittance efficiency is considered and compared with the results under the symmetric choice scenario. The relation between security key generation rate and the total transmission loss is shown with exchanged ratio of the two distances between Alice to the untrusted third party and Bob to the third party. Based on the relationship, an optimal intensity method is proposed to improve the key rate for a fixed distance ratio, which will provide important parameters for practical experiment.

Measurement-device-independent quantum key distribution with odd coherent state

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.

Experimental passive decoy-state quantum key distribution

The decoy-state method is widely used in practical quantum key distribution systems to replace ideal single photon sources with realistic light sources of varying intensities. Instead of active modulation, the passive decoy-state method employs built-in decoy states in a parametric down-conversion photon source, which can decrease the side channel information leakage in decoy-state preparation and hence increase the security. By employing low dark count up-conversion single photon detectors, we experimentally demonstrate the passive decoy-state method over a 50 km long optical fiber and obtain a key rate of about 100 bit s−1. Our result suggests that the passive decoy-state source is a practical candidate for future quantum communication implementation.

Tightened estimation can improve the key rate of measurement-device-independent quantum key distribution by more than 100%

We present formulas that tighten the upper bound for the phase-flip errors in the decoy-state method by using four intensities. Our result compressed the bound to about a quarter of the known result for measurement-device-independent quantum key distribution. Based on this, we find that the key rate is improved by more than 100% given weak coherent state sources, and even more than 200% with heralded single-photon sources.

Passive decoy-state quantum key distribution using weak coherent pulses with intensity fluctuations

Passive decoy-state quantum key distribution (QKD) systems, proven to be more desirable than the active ones in some scenarios, also have the problem of device imperfections like intensity fluctuations. In this paper, the formula of key generation rate of the passive decoy-state protocol using the weak coherent pulse (WCP) source with intensity fluctuation is given, and then the influence of intensity fluctuations on the performance of the passive decoy-state protocol is rigorously characterized. From numerical simulations, it can be seen that intensity fluctuations have non-negligible influence on the performance of the passive decoy-state QKD protocol with WCP source. Most importantly, our simulations show that, under the same deviation of intensity fluctuations, the passive decoy-state method performs better than the active one decoy-state method and is close to the active vacuum + weak decoy-state method.

Proof-of-principle experiment of reference-frame-independent quantum key distribution with phase coding.

We have demonstrated a proof-of-principle experiment of reference-frame-independent phase coding quantum key distribution (RFI-QKD) over an 80-km optical fiber. After considering the finite-key bound, we still achieve a distance of 50 km. In this scenario, the phases of the basis states are related by a slowly time-varying transformation. Furthermore, we developed and realized a new decoy state method for RFI-QKD systems with weak coherent sources to counteract the photon-number-splitting attack. With the help of a reference-frame-independent protocol and a Michelson interferometer with Faraday rotator mirrors, our system is rendered immune to the slow phase changes of the interferometer and the polarization disturbances of the channel, making the procedure very robust.

Analysis of measurement device independent quantum key distribution with an asymmetric channel transmittance efficiency

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.

Measurement-device-independent quantum key distribution with odd coherent state

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 safe. 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.

Three-intensity decoy-state method for measurement-device-independent quantum key distribution

We study the measurement device independent quantum key distribution (MDI-QKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method. We present a more tightened explicit formula to estimate the lower bound of the yield of two-single-photon pulses. Moreover, we show that the bounding of this yield and phase flip error of single photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Results of numerical simulation for key rates with both the improved explicit formula and the program are presented. It shows that the results obtained with our methods here can significantly improve the key rate and secure distance of MDI QKD with only three intensities.

Practical aspects of measurement-device-independent quantum key distribution

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.

Experimental Measurement-Device-Independent Quantum Key Distribution

Quantum key distribution is proven to offer unconditional security in communication between two remote users with ideal source and detection. Unfortunately, ideal devices never exist in practice and device imperfections have become the targets of various attacks. By developing up-conversion single-photon detectors with high efficiency and low noise, we faithfully demonstrate the measurement-device-independent quantum-key-distribution protocol, which is immune to all hacking strategies on detection. Meanwhile, we employ the decoy-state method to defend attacks on a nonideal source. By assuming a trusted source scenario, our practical system, which generates more than a 25 kbit secure key over a 50km fiber link, serves as a stepping stone in the quest for unconditionally secure communications with realistic devices.

A universal quantum key distribution method

Combining heralded pair coherent state (HPCS) with passive decoy-state idea, a new method is presented for quantum key distribution (QKD). The weak coherent source (WCS) and heralded single photon source (HSPS) are the most common photon sources for state-of-the-art QKD. However, there is a prominent crossover between the maximum secure distance and the secure key generation rate if these two sources are applied in a practical decoy-state QKD. The method in this paper does not prepare decoy states actively. Therefore, it uses the same experimental setup as the conventional protocol, and there is no need for a hardware change, so its implementation is very easy. Furthermore, the method can obtain a longer secure transmission distance, and its key generation rate is higher than that of the passive decoy-state method with WCS or HSPS in the whole secure transmission distance. Thus, the limitation of the mentioned photo sources for QKD is broken through. So the method is universal in performance and implementation.

Decoy-state quantum key distribution with biased basis choice.

We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the Z basis and decoy states in the X and Z basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-state scheme. In the postprocessing, we also apply a rigorous method to upper bound the phase error rate of the single-photon components of signal states.

Erratum: Three-intensity decoy-state method for device-independent quantum key distribution with basis-dependent errors [Phys. Rev. A87, 012320 (2013)

Erratum: Three-intensity decoy-state method for device-independent quantum key distribution with basis-dependent errors [Phys. Rev. A87, 012320 (2013)

Practical decoy-state measurement-device-independent quantum key distribution

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.

Decoy-state method for subcarrier-multiplexed frequency-coded quantum key distribution

We propose a decoy-state method to increase key generation rate of frequency-coded (FC) implementation of B92 quantum key distribution (QKD) protocol. Direct application of decoy-state method to FC-QKD results in a security loophole. We overcome this loophole by optimizing the ratio of decoy-to-signal carrier photon number to unity. Simulation results for a single-channel FC-QKD show 16 kbits of raw key length at a transmission distance of 70 km. We then extend the decoy-state method to subcarrier-multiplexed FC-QKD. We show that key generation rate and secure link length improves by a factor of 5 and 40 km, respectively, compared to single-carrier with decoy-state method.

Three-intensity decoy-state method for device-independent quantum key distribution with basis-dependent errors

We study the measurement device independent quantum key distribution (MDIQKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method and when there are basis dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with 3 different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon source such as the coherent states or the heralded states from the parametric down conversion. We point out that the existing result for secure QKD with source coding errors does not always hold. We find that very accurate source coding is not necessary. In particular, we loosen the precision of existing result by several magnitude orders for secure QKD.

Performance analysis of decoy-state quantum key distribution with a heralded pair coherent state photon source

从有效性、稳定性和可行性三个方面, 对基于标记配对相干态光源的诱骗态量子密钥分配的性能进行了全面分析. 采用四组实验数据对基于标记配对相干态光源的三强度诱骗态方案的密钥生成效率、量子比特误码率和最优信号态强度与安全传输距离之间的关系进行了仿真和分析; 考虑到光源涨落, 对方案的稳定性进行了讨论和仿真; 并对基于标记配对相干态光源设计简单易实现方案的可行性进行了分析. 结论表明: 基于标记配对相干态光源的诱骗态方案性能在安全传输距离和密钥生成效率两方面都优于现有基于弱相干态光源和预报单光子源的诱骗态方案; 在光源强度涨落相同条件下, 标记配对相干态光源的稳定性逊于预报单光子源, 而优于相干态光源. 但是标记配对相干态光源在有效性上的优势可弥补其在稳定性上的不足; 且标记配对相干态光源的双模特性为设计简单易实现的被动诱骗态方案提供了条件.