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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Complete bi-partite CV entanglement characterization via coveriance matrix measurement

A. Porzio, Virginia D’Auria, Stefano Fornaro, Salvatore Solimeno

Published Apr 23, 2009• 0 citations
Publisher

Abstract

We report the first complete experimental reconstruction of the covariance matrix (CM) relative to a bi-partite continuous variable (CV) entangled state outing a non degenerate optical parametric oscillator (OPO) below threshold. The covariance matrix CM has been reconstructed following the method reported in V. D'Auria et al., J. Opt. B 7, S750 (2005). The two entangled beams (signal (a) and idler (b)) are produced by a by a continuous wave (CW) optical parametric oscillator (OPO) via type-II (same frequency but with orthogonal polarizations), phase matching and working below threshold. Our experimental setup makes use of a single homodyne detector and of a compact source of entangled beams. The quadratures values and other relevant quantities are reconstructed by quantum tomography, without making any a priori assumption on the state under evalutation.

DOI
10.1117/12.820351

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We report the first complete experimental reconstruction of the covariance matrix (CM) relative to a bi-partite continuous variable (CV) entangled state outing a non degenerate optical parametric oscillator (OPO) below threshold. The covariance matrix CM has been reconstructed following the method reported in V. D'Auria et al., J. Opt. B 7, S750 (2005). The two entangled beams (signal (a) and idler (b)) are produced by a by a continuous wave (CW) optical parametric oscillator (OPO) via type-II (same frequency but with orthogonal polarizations), phase matching and working below threshold. Our experimental setup makes use of a single homodyne detector and of a compact source of entangled beams. The quadratures values and other relevant quantities are reconstructed by quantum tomography, without making any a priori assumption on the state under evalutation.
We present the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement, and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of optical parametric oscillator signals and represent a tool for quantum technology based on continuous variable entanglement.
Gaussian bipartite states are basic tools for the realization of quantum information protocols with continuous variables. Their complete characterization is obtained by the reconstruction of the corresponding covariance matrix. Here we describe in detail and experimentally demonstrate a robust and reliable method to fully characterize bipartite optical Gaussian states by means of a single homodyne detector. We have successfully applied our method to the bipartite states generated by a sub-threshold type-II optical parametric oscillator which produces a pair of thermal cross-polarized entangled cw frequency degenerate beams. The method provides a reliable reconstruction of the covariance matrix and allows us to retrieve all the physical information about the state under investigation. These include observable quantities, such as energy and squeezing, as well as nonobservable ones such as purity, entropy, and entanglement. Our procedure also includes advanced tests for the Gaussianity of the state and, overall, represents a powerful tool to study the bipartite Gaussian state from the generation stage to the detection one.
In a recent paper by D'Auria et al (2009 Phys. Rev. Lett. 102 020502) we reported the full experimental reconstruction of Gaussian entangled states generated by a type-II optical parametric oscillator (OPO) below threshold using a single homodyne detector. Here we investigate more deeply the Gaussian character of the OPO output addressing the homodyne traces. More precisely, we apply a suitable normality test to check the actual Gaussian distribution of the homodyne data and then we perform the full reconstruction of the signal.