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Physical Review A

Experimental demonstration of counteracting imperfect sources in a practical one-way quantum-key-distribution system

Fang-Xing Xu, Yang Zhang, Zheng Zhou, Wei Qiu Chen, Zheng‐Fu Han, Guang‐Can Guo

Published Dec 4, 2009• 21 citations
Publisher

Abstract

In a practical quantum-key-distribution system, photon source and small operational errors cause intensity fluctuations inevitably, which cannot be ignored for a precise estimation on the single-photon fraction. In this paper, we demonstrated an efficient three-intensity decoy method scheme on top of the one-way Faraday-Michelson Interferometric system, combining an active monitoring with existing commercial apparatus to inspect fluctuations instantly. With this faithful detection for the upper bound of the fluctuation, the secure quantum key distribution is unconditionally realized with whatever type of intensity errors, which declares the utility and potential of decoy theory and active monitoring for quantum key distribution in practical use.

DOI
10.1103/physreva.80.062309

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In a practical quantum-key-distribution system, photon source and small operational errors cause intensity fluctuations inevitably, which cannot be ignored for a precise estimation on the single-photon fraction. In this paper, we demonstrated an efficient three-intensity decoy method scheme on top of the one-way Faraday-Michelson Interferometric system, combining an active monitoring with existing commercial apparatus to inspect fluctuations instantly. With this faithful detection for the upper bound of the fluctuation, the secure quantum key distribution is unconditionally realized with whatever type of intensity errors, which declares the utility and potential of decoy theory and active monitoring for quantum key distribution in practical use.
The decoy-state method closes source security loopholes in quantum key distribution (QKD) using a laser source. In this method, accurate estimates of the detection rates of vacuum and single-photon events plus the error rate of single-photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 11%1 relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key rate of the BB84 QKD protocol with unbiased bases selection by at least 20% on average in realistic settings. The major tricks are the use of more than three types of photon intensities plus the fact that estimating bounds of the above detection and error rates is numerically stable, although these bounds are related to the inversion of a high condition number matrix.
A passive scheme with a photon-number-resolving detector and a beam splitter which are used to monitor the statistical characteristics of photon source, is proposed to verify the security of three-intensity decoy-state quantum key distribution system with an untrusted source. The practical issues due to statistical fluctuation and detection noise are analyzed. The simulation results show that the scheme can work efficiently when the data size N≥108N\ge10^{8}N≥108 and the dark count rate of the detector is below 0.5 counts/pulse, which are realizable by current techniques. We also give an experimental example of PNR detector which is easily realized by a variable optical attenuator combined with a practical threshold detector.
We present an improved formula for the lower bound of the fraction of single-photon counts in a decoy-state protocol with an unstable source. Based on the formula, we study two-intensity protocol and three-intensity protocol. The major formula in the passive two-intensity protocol proposed by Adachi, Yamamoto, Koashi, and Imoto (AYKI) [Phys. Rev. Lett. 99, 180503 (2007)] actually always holds with whatever intensity fluctuation of pump light. Therefore, the protocol can always work securely without monitoring the source state or switching the source intensity. We also show that our result can greatly improve the key rate of the three-intensity protocol with a fluctuating coherent-state source.
Secure quantum key distribution can be achieved with an imperfect single-photon source through implementing the decoy-state method. However, security of all those theoretical results of decoy-state method based on the original framework raised by Hwang needs monitoring the source state very carefully, because the elementary proposition that the counting rates of the same state from different sources are equal does not hold in general when the source is unstable. Source intensity monitoring greatly decreases the system efficiency. Here without using Hwang's proposition for stable source, we present a sufficient condition for a secure decoy-state protocol without monitoring the source intensity. The passive 2-intensity protocol proposed by Adachi, Yamamoto, Koashi, and Imoto(AYKI) (Phys. Rev. Lett. 99, 180503 (2007) satisfies the condition. Therefore, the protocol can always work securely without monitoring the source state or switching the source intensity. We also show that our result can greatly improve the key rate of the 3-intensity protocol with a fluctuating coherent-state source.
We present a review on the historic development of the decoy state method, including the background, principles, methods, results and development. We also clarify some delicate concepts. Given an imperfect source and a very lossy channel, the photon-number-splitting (PNS) attack can make the quantum key distribution (QKD) in practice totally insecure. Given the result of ILM-GLLP, one knows how to distill the secure final key if he knows the fraction of tagged bits. The purpose of decoy state method is to do a tight verification of the the fraction of tagged bits. The main idea of decoy-state method is changing the intensities of source light and one can verify the fraction of tagged bits of certain intensity by watching the the counting rates of pulses of different intensities. Since the counting rates are small quantities, the effect of statistical fluctuation is very important. It has been shown that 3-state decoy-state method in practice can work even with the fluctuations and other errors.
Quantum key distribution (QKD) theoretically offers unconditional security. Unfortunately, the gap between theory and practice threatens side-channel attacks on practical QKD systems. Many well-known QKD protocols use weak coherent laser pulses to encode the quantum information. These sources differ from ideal single photon sources and follow Poisson statistics. Many protocols, such as decoy state and coincidence detection protocols, rely on monitoring the photon statistics to detect any information leakage. The accurate measurement and characterization of photon statistics enable the detection of adversarial attacks and the estimation of secure key rates, strengthening the overall security of the QKD system. We have rigorously characterized our source to estimate the mean photon number employing multiple detectors for comparison against measurements made with a single detector. Furthermore, we have also studied intensity fluctuations to help identify and mitigate any potential information leakage due to state preparation flaws. We aim to bridge the gap between theory and practice to achieve information-theoretic security.