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arXiv:2109.13830 · Physical Review A

Security bounds for decoy-state quantum key distribution with arbitrary photon-number statistics

Giulio Foletto, Francesco Picciariello, Costantino Agnesi, Paolo Villoresi, Giuseppe Vallone

Published Jan 6, 2022• 14 citations
arXivHTMLPDF

Abstract

Typically, descriptions of decoy-state quantum key distribution involve the assumption of Poissonian photon-number statistics. Here, the authors extend this to an arbitrary distribution in order to better model implementations that use non--laser light source technology, like LEDs and quantum dots.
DOI
10.1103/physreva.105.012603

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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.
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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.
Every security analysis of quantum-key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, such as for instance a parametric down-conversion (PDC) source, require a multimode description but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive bounds on the single-photon transmission probability and error rate for multimode states and apply these bounds to the output state of a PDC source. We observe two opposing effects on the secure key rate. First, the multimode structure of the state gives rise to a new attack that decreases the key rate. Second, more contributing modes change the photon number distribution from a thermal toward a Poissonian distribution, which increases the key rate.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.