Degree of polarization and quantum-mechanical purity

H Moya-Cessa,J.R Moya-Cessa,A T Friberg,J E A Landgrave,G Mart\'{\I,A P\'Erez-Leija

doi:10.2971/jeos.2008.08014

Abstract

The purity parameter is used in quantum mechanics to discriminate pure states from mixed states. We employ this concept to define a degree of polarization for general, three-dimensional, classical random electric fields. Our approach leads to a result that is identical with a recent definition obtained by a decomposition of the polarization matrix in terms of the Gell-Mann matrices. We also give an expression for this degree of polarization based on the constituent two-dimensional subsystems.

Highlights

The fact that the paraxial approximation to the Helmholtz equation leads to a Schrodinger equation may be responsible for the many analogies that are found between quantum physics and classical optics
The representation of the 3 × 3 polarization matrix by the Gell-Mann matrices is formally analogous to the expansion of the 2 × 2 polarization matrix by the Pauli matrices, [8] leading to the Stokes parameters and the usual degree of polarization for beams. [4]-[6] The expression in Eq (1) has been obtained by Luis [13] by formulating the degree of polarization as a vector-space distance between the field’s polarization matrix and the identity matrix. In this contribution we show that on borrowing the concept of purity from quantum mechanics, one directly obtains the degree of polarization given in Eq (1)
I

Summary

Perez-Leija

The purity parameter is used in quantum mechanics to discriminate pure states from mixed states. We employ this concept to define a degree of polarization for general, three-dimensional, classical random electric fields. Our approach leads to a result that is identical with a recent definition obtained by a decomposition of the polarization matrix in terms of the Gell-Mann matrices. We give an expression for this degree of polarization based on the constituent two-dimensional subsystems.

INTRODUCTION

ENTROPY AND PURITY

CONCLUSIONS