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Evaluation of photon number distribution for security certification of decoy quantum key distribution

Ryoji Matsumoto, TAKUMI MATSUURA, Atsushi Okamoto, Akihisa Tomita

Published May 27, 2026• 0 citations

Abstract

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.

DOI: 10.1364/oe.593332

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High-speed light source is realized for decoy-state quantum key distribution(QKD) at telecom wavelength of 1.55 μm. By implementing two different electrical pulses together and triggering with 100 MHz pseudorandom number to drive the laser diode, the signal-state and the decoy-state pulses are prepared with identical pulse duration of 25 ps and similar spectral characteristics, avoiding the eavesdropper’s attack by temporal and spectral analysis. The intensity fluctuation of the light source is quantified to satisfy the practical decoy-state QKD with random intensity error. The characteristics of the light source are analyzed with a high-speed single-photon detector.

The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.

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.

High-speed light source is realized for decoy-state quantum key distribution (QKD) at telecom wavelength of 1.55 µm.By implementing two different electrical pulses together and triggering with 100 MHz pseudorandom number to drive the laser diode, the signal-state and the decoy-state pulses are prepared with identical pulse duration of 25 ps and similar spectral characteristics, avoiding the eavesdropper's attack by temporal and spectral analysis.The intensity fluctuation of the light source is quantified to satisfy the practical decoy-state QKD with random intensity error.The characteristics of the light source are analyzed with a high-speed single-photon detector.