A New Mathematical Framework for CMOS Si Photomultiplier Detection Rates in Quantum Cryptography

The deployment of Discrete Variable Quantum Key Distribution (DV-QKD) in high-traffic, short-reach environments, such as intra-data center networks, is currently constrained by the saturation of single-photon detectors. While CMOS Single-Photon Avalanche Diodes (SPADs) offer a cost-effective solution, their Secure Key Rate (SKR) is limited by detector dead time. To the best of the authors' knowledge, this work is the first to derive a generalized detection rate model for SiPMs that addresses the dead-time bottlenecks of gigahertz-rate quantum cryptography. While methods for managing deadtime via active optical switching have been proposed, our model quantifies the benefits of passive spatial multiplexing inherent in standard SiPM arrays. Furthermore, contrasting with models designed to optimize energy resolution or characterize nonlinear charge response to light pulses, our work focuses on maximizing the detection count rate. We derive exact detection rate models for both analog (paralyzable) and digital (non-paralyzable) SiPM architectures, incorporating correlated noise sources such as optical crosstalk and afterpulsing. Simulation results indicate that SiPMs can increase detection rates by over an order of magnitude compared to single SPADs.