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Physical Review A

Characterizing photon-number distribution of pulsed sources using non–photon-number-resolving detectors for quantum key distribution

Yang-Guang Shan, Guan‐Jie Fan‐Yuan, Shuang Wang, Wei Chen, De‐Yong He, Zhen−Qiang Yin, Guang‐Can Guo, Zheng‐Fu Han

Published Sep 9, 2021• 4 citations
Publisher

Abstract

Quantum key distribution (QKD) has a prospect to realize unconditional secure communication. However, many real system problems should be solved. Transmitters security is an important part of QKD security. And measuring photon number distribution could help improve it. This measurement is also useful for measuring unknown sources or testing newly designed sources. In this article, a method to measure the photon number distribution of pulses using non-photon-number-resolving detectors is proposed. Numerical simulation is conducted to test this scheme and performs well. Experiment on Poisson source is also used to test this method.

DOI
10.1103/physreva.104.032406

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Quantum key distribution (QKD) has a prospect to realize unconditional secure communication. However, many real system problems should be solved. Transmitters security is an important part of QKD security. And measuring photon number distribution could help improve it. This measurement is also useful for measuring unknown sources or testing newly designed sources. In this article, a method to measure the photon number distribution of pulses using non-photon-number-resolving detectors is proposed. Numerical simulation is conducted to test this scheme and performs well. Experiment on Poisson source is also used to test this method.
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.
Characterizing the input-output photon-number distribution of an unknown optical quantum channel is a worthwhile task for many applications in quantum information processing. Ideally, this would require deterministic photon-number sources and photon-number-resolving detectors, but these technologies are still work in progress. In this work, we propose a general method to rigorously bound the input-output photon-number distribution of an unknown optical channel using standard optical devices such as coherent light sources and non-photon-number-resolving detectors and homodyne detectors. To demonstrate the broad utility of our method, we consider the security analysis of practical quantum key distribution systems based on calibrated single-photon detectors and an experimental proposal to implement time-correlated single-photon counting technology using homodyne detectors instead of single-photon detectors.
Decoy-state quantum key distribution (QKD) requires information about the photon number distribution of the light sources. The photon number distribution of weak coherent photon sources has been assumed to follow a Poisson distribution. However, it is not yet clear whether picosecond laser pulses, used in high-speed QKD systems, satisfy this assumption due to the significant and rapid changes in carrier density and photon density in the laser cavity. It is necessary to establish a method to experimentally evaluate the photon number distribution of laser pulses with a duration of less than 100 ps. We have implemented three methods to identify a suitable approach for evaluating light sources in quantum key distribution systems. Our findings indicate that all three methods conclude that the photon numbers of the gain-switching laser pulse are consistent with a Poisson distribution. We then compared these methods based on their accuracy of photon number probability and ease of implementation. These considerations will establish a method suitable for the security certification of high-speed quantum key distributed devices.
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.
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source’s photon statistics and use it in the estimation of a quantum key distribution system’s key rate. This promises to be a useful tool for the certification of quantum-related technologies.
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to derive the secure key rate of quantum key distribution systems. Hence the photon number distribution of the light source can directly impact the randomness and the security distilled from such devices. Here, we propose a method based on measuring correlation functions to experimentally characterize a light source's photon statistics and use it in the estimation of a quantum key distribution system's key rate. This promises to be a useful tool for the certification of quantum-related technologies.