Probing light polarization with the quantum Chernoff bound

TL;DR

This paper introduces a quantum polarization measure based on the quantum Chernoff bound, providing explicit formulas and comparisons with other measures, enhancing understanding of quantum light polarization.

Contribution

It develops a new quantum polarization measure using the quantum Chernoff bound and compares it with existing measures, offering insights into quantum polarization characterization.

Findings

Derived explicit expression for the quantum Chernoff bound-based polarization measure.

Compared Chernoff and Bures degrees of polarization for specific quantum states.

Provided illustrative examples demonstrating differences between polarization measures.

Abstract

We recall the framework of a consistent quantum description of polarization of light. Accordingly, the degree of polarization of a two-mode state $\hat \rho$ of the quantum radiation field can be defined as a distance of a related state ${\hat \rho}_b$ to the convex set of all SU(2) invariant two-mode states. We explore a distance-type polarization measure in terms of the quantum Chernoff bound and derive its explicit expression. A comparison between the Chernoff and Bures degrees of polarization leads to interesting conclusions for some particular states chosen as illustrative examples.