Modeling of single-photon avalanche diode photon counts from spontaneous parametric down-conversion using fractional Poisson processes

Document Type

Article

Publication Date

1-1-2026

Abstract

This work introduces a novel, to our knowledge, approach using a dead-time-modified generalized fractional Poisson process (GFPP) to model the interarrival time statistics of photon counts from a spontaneous parametric down-conversion (SPDC) light source. The model accurately describes the experimental interarrival time histograms across a range of photon count rates, with power-law behavior at short timescales and exponential decay at long timescales. The analysis of the fitted parameters (xi, alpha and beta) reveals that the detection process can be characterized as a dead-time-modified Erlang-type process (beta approximate to 1), where the fractional order 0 < alpha < 1 quantifies the temporal clustering of photon detection events attributed to afterpulsing and twilight pulses. Cross-validation through Monte Carlo simulations confirms that the photon count distributions are consistent with the interarrival time analysis.

Keywords

Quantum key distribution, Photodiodes

Publication Title

Journal of the Optical Society of America B

ISSN

0740-3224

DOI

10.1364/JOSAB.577382

Volume

43

Issue

1

First Page

189

Last Page

198

Publisher

Optica Publishing Group

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