Wigner representation for polarization-momentum hyperentanglement generated in parametric down conversion, and its application to complete Bell-state measurement

TL;DR

This paper uses the Wigner function formalism to analyze polarization-momentum hyperentanglement in photon pairs generated by parametric down conversion, providing insights into Bell-state measurement limitations and the role of zeropoint fields.

Contribution

It introduces a comprehensive Wigner function approach to describe hyperentangled states and analyzes the impact of zeropoint modes on Bell-state measurement capabilities.

Findings

Describes quantum correlations for all sixteen Bell states.

Highlights the role of zeropoint fields in entanglement and measurement.

Identifies limits on Bell-state measurement efficiency due to zeropoint contributions.

Abstract

We apply the Wigner function formalism to the study of two-photon polarization-momentum hyperentanglement generated in parametric down conversion. It is shown that the consideration of a higher number of degrees of freedom is directly related to the extraction of additional uncorrelated sets of zeropoint modes at the source. We present a general expression for the description of the quantum correlations corresponding to the sixteen Bell base states, in terms of four beams whose amplitudes are correlated through the stochastic properties of the zeropoint field. A detailed analysis of the two experiments on complete Bell-state measurement included in [Walborn et al., Phys. Rev. A 68, 042313 (2003)] is made, emphasizing the role of the zeropoint field. Finally, we investigate the relationship between the zeropoint inputs at the source and the analysers, and the limits on optimal Bell-state measurement.