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

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 K.