Quantifying the non-Gaussianity of the state of spatially correlated down-converted photons

TL;DR

This paper investigates the non-Gaussian features of spatially correlated down-converted photons, introducing a negentropy-based measure to quantify non-Gaussianity and analyzing its implications for quantum information applications.

Contribution

It presents a new statistical measure based on negentropy to quantify non-Gaussianity in SPDC photon states, considering phase-matching effects and entanglement detection.

Findings

Phase-matching influences the spatial distribution variances.

Negentropy measure effectively quantifies non-Gaussianity.

The method requires only autocorrelation covariance measurements.

Abstract

The state of the spatially correlated down-converted photons is usually treated as a two-mode Gaussian entangled state. While intuitively this seems to be reasonable, it is known that new structures in the spatial distributions of these photons can be observed when the phase-matching conditions are properly taken into account. Here, we study how the variances of the near- and far-field conditional probabilities are affected by the phase-matching functions, and we analyze the role of the EPR-criterion regarding the non-Gaussianity and entanglement detection of the spatial two-photon state of spontaneous parametric down-conversion (SPDC). Then we introduce a statistical measure, based on the negentropy of the joint distributions at the near- and far-field planes, which allows for the quantification of the non-Gaussianity of this state. This measure of non-Gaussianity requires only the measurement of the autocorrelation covariance sub-matrices, and will be relevant for new applications of the spatial correlation of SPDC in CV quantum information processing.