Advances in Mathematical Physics
Volume 2010 (2010), Article ID 501521, 11 pages
Research Article

Partial Bell-State Analysis with Parametric down Conversion in the Wigner Function Formalism

1Departamento de Física Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, 41092 Sevilla, Spain
2Centro Asociado de la Universidad Nacional de Educación a Distancia de Las Palmas de Gran Canaria, 35004 Las Palmas de Gran Canaria, Spain
3Departamento de Física, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain

Received 2 October 2009; Accepted 11 October 2009

Academic Editor: Adan Cabello

Copyright © 2010 A. Casado et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We apply the Wigner function formalism to partial Bell-state analysis using polarization entanglement produced in parametric down conversion. Two-photon statistics at a beam-splitter are reproduced by a wave-like description with zeropoint fluctuations of the electromagnetic field. In particular, the fermionic behaviour of two photons in the singlet state is explained from the invariance on the correlation properties of two light beams going through a balanced beam-splitter. Moreover, we show that a Bell-state measurement introduces some fundamental noise at the idle channels of the analyzers. As a consequence, the consideration of more independent sets of vacuum modes entering the crystal appears as a need for a complete Bell-state analysis.