Quantum versus classical polarization states: when multipoles count

TL;DR

This paper introduces a multipole expansion approach for polarization states, enabling the construction of quasiprobability distributions that capture higher-order polarization correlations beyond classical descriptions.

Contribution

It presents a novel multipole expansion framework for polarization density matrices and develops a hierarchy of measures for higher-order polarization correlations.

Findings

Multipole expansion effectively characterizes polarization states.

Hierarchy of measures quantifies higher-order polarization correlations.

Q function-based approach links classical and quantum polarization descriptions.

Abstract

We advocate for a simple multipole expansion of the polarization density matrix. The resulting multipoles are used to construct bona fide quasiprobability distributions that appear as a sum of successive moments of the Stokes variables; the first one corresponding to the classical picture on the Poincare sphere. We employ the particular case of the $Q$ function to formulate a whole hierarchy of measures that properly assess higher-order polarization correlations.