Measures of Quantum State Purity and Classical Degree of Polarization

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.