Measures of Quantum State Purity and Classical Degree of Polarization

TL;DR

This paper explores the mathematical analogy between classical polarization and quantum states, analyzing various measures of polarization and purity, and proposing new entanglement measures based on subsystem purity.

Contribution

It extends the analogy to higher dimensions, compares existing polarization measures, and introduces a novel class of entanglement measures based on subsystem purity.

Findings

Different polarization measures show unique advantages in higher dimensions.

The analogy clarifies the relationship between classical polarization and quantum purity.

Proposed entanglement measures based on subsystem purity offer new insights.

Abstract

There is a well-known mathematical similarity between two-dimensional classical polarization optics and two-level quantum systems, where the Poincare and Bloch spheres are identical mathematical structures. This analogy implies that the classical degree of polarization and quantum purity are in fact the same quantity. We make extensive use of this analogy to analyze various measures of polarization for higher dimensions proposed in the literature, in particular the $N = 3$ case, illustrating interesting relationships that emerge as well as the advantages of each measure. We also propose a different class of measures of entanglement based on the purity of subsystems.