Negativity of the Wigner function and thermal effects of Bell-Cat states

TL;DR

This paper investigates how thermal effects influence the non-classical properties of Bell-Cat states by analyzing their Wigner functions at different temperatures using Thermofield Dynamics.

Contribution

It introduces a method to compute thermal Wigner functions for Bell-Cat states and studies the temperature dependence of their non-classical features.

Findings

Non-classical properties diminish around 2 K.

Thermal effects significantly reduce Wigner function negativity.

Non-classicality is nearly absent at higher temperatures.

Abstract

We applied the Thermofield Dynamics formalism to analyze how the non-classical properties of the Bell-Cat states are influenced by a gradual change of temperature values, in a thermal equilibrium system. To this purpose we calculate the thermal Wigner functions for these states, whose negative volume is associated with non-classical properties, and we evaluate how these non-classical features vary with temperature. Our results indicate that these properties are almost absent for temperatures of around $2\mathrm{K}$.