Developing a practical model for noise in entangled photon detection

TL;DR

This paper presents a detailed model for noise and detection effects in entangled photon experiments, enabling more accurate analysis and design of quantum optics setups with realistic detector imperfections.

Contribution

It introduces a comprehensive model for the two-photon density matrix considering various detector configurations and nonidealities, including analytic solutions for PNR detectors.

Findings

Four detectors improve fidelity compared to two detectors.

PNR detectors offer minimal advantage over threshold detectors in studied regimes.

The model enables quantitative design of experiments with realistic noise sources.

Abstract

We develop a comprehensive model for the effective two-photon density matrix produced by a parametric source of entangled photon pairs under a variety of detector configurations commonly seen in a laboratory setting: two and four photon number-resolving (PNR) and threshold detectors. We derive the probability of obtaining a single coincidence assuming Poisson-distributed photon pairs, non-unit detection efficiency, and dark counts; obtain the effective density matrix; and use this quantity to compute the fidelity of the generated quantum state. The 4 PNR case admits an analytic result valid for any combination of parameters, while all other cases leverage low-efficiency approximations to arrive at closed-form expressions. Interestingly, our model reveals appreciable fidelity improvements from four detectors as opposed to two yet minimal advantages for PNR over threshold detectors in the regimes explored. Overall, our work provides a valuable tool for the quantitative design of two-photon experiments under realistic nonidealities.