Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurements

TL;DR

This paper explores the properties of biphoton polarization-frequency ququarts, showing how their states can appear pure or mixed depending on measurement type, and proposes schemes for their reconstruction from coincidence measurements.

Contribution

It introduces a detailed analysis of biphoton ququarts' features and proposes new schemes for their state reconstruction based on coincidence measurements.

Findings

Pure states can appear as mixed states under polarization measurements.

Features depend on whether polarization or polarization-frequency measurements are used.

Schemes for reconstructing ququart parameters are proposed and described.

Abstract

Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, biphoton ququarts can display different features in dependence on whether experiments involve purely polarization or (alternatively) polarization-frequency measurements. If in experiments one uses only polarization measurements, the originally pure states of ququarts can be seen as mixed biphoton polarization states. Features of such states are described and discussed in details. Schemes of coincidence measurements for reconstruction of the ququart's parameters are suggested and described.