Nonclassicality of a single quantum excitation of a thermal field in thermal environments

The nonclassicality of single photon-added thermal states in the thermal channel is investigated by exploring the volume of the negative part of the Wigner function. The Wigner functions become positive when the decay time exceeds a threshold value γtcγtc, which only depends on the effective temperature of the thermal channel. Furthermore, we firstly demonstrate γtcγtc is the same for arbitrary pure or mixed nonclassical optical fields with zero population in vacuum state.