Physics – Quantum Physics
Scientific paper
2011-11-17
Optics Express Vol. 20, Issue 4, pp. 3753-3772 (2012)
Physics
Quantum Physics
20 pages, 5 figures
Scientific paper
10.1364/OE.20.003753
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.
Gómez E. S.
Lima George
Monken Carlos H.
Nogueira W. A. T.
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