Modification of polarization through de-Gaussification

TL;DR

This paper investigates how de-Gaussification, via photon addition, affects the polarization of quantum thermal states, revealing that certain polarization measures show enhancement while others are inconsistent.

Contribution

It introduces and compares multiple polarization degrees, including new entropy-based measures, and demonstrates that Bures and relative entropy metrics reliably indicate polarization enhancement.

Findings

Bures and relative entropy measures show polarization enhancement after de-Gaussification.

Some popular polarization degrees are inconsistent with the more robust measures.

Photon-added states exhibit increased polarization compared to original thermal states.

Abstract

We analyze the polarization of a quantum radiation field under a de-Gaussification process. Specifically, we consider the addition of photons to a two-mode thermal state to get mixed non-Gaussian and nonclassical states which are still diagonal in the Fock basis. Stokes-operator-based degrees of polarization and two distance-type measures defined with Hilbert-Schmidt and Bures metrics are investigated. For a better insight we here introduce a polarization degree based on the relative entropy. Polarization of the thermal states is fully investigated and simple closed expressions are found for all the defined degrees. The evaluated degrees for photon-added states are then compared to the corresponding ones for the two-mode thermal states they originate from. We present interesting findings which tell us that some popular degrees of polarization are not fully consistent. However, the most solidly defined degrees, which are based on the Bures metric and relative entropy, clearly indicate an enhancement of polarization through de-Gaussification. This conclusion is supported by the behavior of the degrees of polarization of the Fock states, which are finally discussed as a limit case.