Quantifying the non-Gaussianity of the state of spatially correlated down-converted photons
arXiv:1111.4006 · doi:10.1364/OE.20.003753
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.
20 pages, 5 figures
References in corpus (8)
- Spatial correlations in parametric down-conversion
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- Quantifying non-Gaussianity for quantum information
- Transverse Entanglement Migration in Hilbert Space
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Cited by in corpus (5)
- Generalized Hermite-Gauss decomposition of the two-photon state produced by spontaneous parametric down-conversion
- Generating arbitrary photon-number entangled states for continuous-variable quantum informatics
- Maximizing the Validity of the Gaussian Approximation for the biphoton State from Parametric Downconversion
- Non-Gaussian state generation certified using the EPR-steering inequality
- Tunable entanglement distillation of spatially correlated down-converted photons