Partial Bell-state analysis with parametric down conversion in the Wigner function formalism

TL;DR

This paper uses the Wigner function formalism to analyze partial Bell-state measurements with polarization-entangled photons from parametric down conversion, explaining fermionic behavior and noise effects in the process.

Contribution

It demonstrates how the Wigner function formalism can model partial Bell-state analysis and explains the origin of noise and fermionic behavior in the measurement process.

Findings

Reproduces two-photon statistics with a wave-like model.

Explains fermionic behavior of singlet state photons.

Identifies fundamental noise introduced during Bell-state measurement.

Abstract

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 wavelike 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.