Analysis of Elliptically Polarized Maximally Entangled States
for Bell Inequality Tests¹

A. Martin^a, J.-L. Smirr^b, F. Kaiser^a, E. Diamanti^b, A. Issautier^a, O. Alibart^a,
R. Frey^b, I. Zaquine^b, *, and S. Tanzilli^a, **

^a Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université de Nice—Sophia Antipolis,
Parc Valrose, 06108 Nice Cedex 2, France

^b Laboratoire Traitement et Communication de l’Information, CNRS UMR 5141,
Institut Mines Télécom/Télécom ParisTech, 46 rue Barrault, 75013 Paris, France

*e-mail: isabelle.zaquine@telecom-paristech.fr
**e-mail: sebastien.tanzilli@unice.fr

Received December 17, 2011; published online May 11, 2012

Abstract—When elliptically polarized maximally entangled states are considered, i.e., states having a non ran-
dom phase factor between the two bipartite polarization components, the standard settings used for optimal vio-
lation of Bell inequalities are no longer adapted. One way to retrieve the maximal amount of violation is to com-
pensate for this phase while keeping the standard Bell inequality analysis settings. We propose in this paper a
general theoretical approach that allows determining and adjusting the phase of elliptically polarized maximally
entangled states in order to optimize the violation of Bell inequalities. The formalism is also applied to several
suggested experimental phase compensation schemes. In order to emphasize the simplicity and relevance of our
approach, we also describe an experimental implementation using a standard Soleil-Babinet phase compensa-
tor. This device is employed to correct the phase that appears in the maximally entangled state generated from
a type-II nonlinear photon-pair source after the photons are created and distributed over fiber channels.

DOI: 10.1134/S1054660X12060060

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