Optimizing the signal-to-noise ratio of biphoton distribution measurements

TL;DR

This paper derives formulas to optimize the measurement of biphoton joint probability distributions using single-photon cameras, enhancing speed and accuracy in high-dimensional quantum optics experiments.

Contribution

It provides a general analytical framework for optimizing data collection parameters to maximize SNR in biphoton measurements, valid beyond low-count regimes.

Findings

Derived expressions for biphoton joint probability and SNR.

Validated the model with experimental data.

Identified optimal operating parameters for measurements.

Abstract

Single-photon-sensitive cameras can now be used as massively parallel coincidence counters for entangled photon pairs. This enables measurement of biphoton joint probability distributions with orders-of-magnitude greater dimensionality and faster acquisition speeds than traditional raster scanning of point detectors; to date, however, there has been no general formula available to optimize data collection. Here we analyze the dependence of such measurements on count rate, detector noise properties, and threshold levels. We derive expressions for the biphoton joint probability distribution and its signal-to-noise ratio (SNR), valid beyond the low-count regime up to detector saturation. The analysis gives operating parameters for global optimum SNR that may be specified prior to measurement. We find excellent agreement with experimental measurements within the range of validity, and discuss discrepancies with the theoretical model for high thresholds. This work enables optimized measurement of the biphoton joint probability distribution in high-dimensional joint Hilbert spaces.