Optimizing the signal-to-noise ratio of biphoton distribution measurements. (arXiv:1802.00489v1 [physics.ins-det])

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.

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