title: Quantifying the non-Gaussianity of the state of spatially correlated down-converted photons.
abstract: The state of 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 diagonal covariance sub-matrices, and will be relevant for new applications of the spatial correlation of SPDC in CV quantum information processing.
authors.affiliation: Departamento de Física, Universidad de Concepcíon, 160-C Concepcíon, Chile.
authors.forename: E S
authors.initials: ES
authors.lastname: Gómez
authors.forename: W A T
authors.initials: WA
authors.lastname: Nogueira
authors.forename: C H
authors.initials: CH
authors.lastname: Monken
authors.forename: G
authors.initials: G
authors.lastname: Lima