Invariant indices of polarimetric purity. Generalized indices of purity for nxn covariance matrices

TL;DR

This paper introduces a set of invariant indices derived from eigenvalues of the coherency matrix to quantify the polarimetric purity of light and media, generalizing existing measures for nxn matrices.

Contribution

It defines a new, comprehensive set of purity indices based on eigenvalues, applicable to nxn systems, with a nested structure that fully characterizes statistical purity.

Findings

Indices relate directly to eigenvalues of the coherency matrix

The indices provide a complete measure of system purity

Generalization to nxn positive semidefinite Hermitian matrices

Abstract

A proper set of indices characterizing the polarimetric purity of light and material media is defined from the eigenvalues of the corresponding coherency matrix. A simple and generalizable relation of these indices with the current parameters characterizing the global purity is obtained. A general definition for systems characterized by nxn positive semidefinite Hermitian matrices is introduced in terms of the corresponding eigenvalues and diagonal Gell-Mann matrices. The set of n-1 indices of purity has a nested structure and provide complete information about the statistical purity of the system.