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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 3753–3772

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

E. S. Gómez, W. A. T. Nogueira, C. H. Monken, and G. Lima  »View Author Affiliations


Optics Express, Vol. 20, Issue 4, pp. 3753-3772 (2012)
http://dx.doi.org/10.1364/OE.20.003753


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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.

© 2012 OSA

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: December 12, 2011
Revised Manuscript: January 22, 2012
Manuscript Accepted: January 23, 2012
Published: January 31, 2012

Citation
E. S. Gómez, W. A. T. Nogueira, C. H. Monken, and G. Lima, "Quantifying the non-Gaussianity of the state of spatially correlated down-converted photons," Opt. Express 20, 3753-3772 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-3753


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