Majorization of quantum polarization distributions

TL;DR

This paper explores using majorization to classify quantum polarization fluctuations, comparing classical and quantum states, and testing conjectures about polarization and nonclassicality.

Contribution

It introduces majorization as a new meta-measure for quantum polarization and evaluates classical-like and pure states against key conjectures.

Findings

Majorization effectively classifies polarization fluctuations.

Classical-like states tend to be the most polarized.

Unpolarized pure states are often the most nonclassical.

Abstract

Majorization provides a rather powerful partial-order classification of probability distributions depending only on the spread of the statistics, and not on the actual numerical values of the variable being described. We propose to apply majorization as a meta-measure of quantum polarization fluctuations, this is to say of the degree of polarization. We compare the polarization fluctuations of the most relevant classes of quantum and classical-like states. In particular we test Lieb's conjecture regarding classical-like states as the most polarized and a complementary conjecture that the most unpolarized pure states are the most nonclassical.