Optimizing the signal-to-noise ratio of biphoton distribution 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 highdimensional joint Hilbert spaces.

Polarization entanglement-enabled quantum holography

“…The peak value is proportional to the mean value of an intensity correlation image measured in the same conditons (i.e.signal of the SNR). The standard deviation of noise in the pixels surrounding the peak is proportional to the standard deviation of the noise in an intensity correlation image acquired in the same condi- [55] shows that the SNR varies as 1{xI cl y.…”

“…For a fixed exposure time and pump power, the SNR varies as ? N , where N is the number of images used to reconstruct the intensity correlation images [55]. In the presence of stray light, the SNR decreases as 1{xI cl y, where xI cl y is the average intensity of classical light falling on the sensor [31,32].…”

“…To characterise the photon pair rate of the source, a threshold is applied on the EM-CCD camera: in each acquired images, all grey values bellow 210 are set to 0 and all values above are set to 1. As detailed in [55], this approach turns the EMCCD into a multi-pixel photon counter with an effective quantum efficiency of 0.61. By acquiring a total of 7000 frames with an exposure time of 3ms (no pattern on the SLM and after removing the polarisers), we measure an average photon rate of 304 photons per second per pixel and an average number of pairs of 0.1 pairs per pixel per second (spatial mode = 1.1 pixels, as shown in Fig.…”

Imaging and certifying high-dimensional entanglement with a single-photon avalanche diode camera

“…As detailed in the 'Methods' section, σ is calculated from the standard deviation of the noise surrounding the coincidence peaks in the sum-and minus-coordinate projections of the JPD. For a fixed exposure time and a constant source intensity, σ depends only on the number of frames acquired to compute the JPD 43 . Figure 4a shows that the measured values of C for different total number of frames N (black crosses) are found to scale as ffiffiffi ffi N p (blue dashed curve, see 'Methods').…”

“…(13) to show that σ ∝ Σ. Finally, we use the fact that Reichert et al 43 have shown that Σ / 1= ffiffiffi ffi N p for a constant average pump power and a fixed exposure time. Thus, we conclude that C / ffiffiffi ffi N p : As shown in Fig.…”