Non-classical properties of superposition thermal quantum states

We study the statistical properties of non-classical states introduced by the superposition of a coherent with a number (Fock) state, in contact with a heat-bath. Two situations are investigated: one starts with the Gibbs distribution, such that photons are added in; the other, photons are subtracted out. Considering the use of such states in protocols for, as an example, teleportation, we identify the range of temperature, where the quantum nature of such states is stable. Finally, we propose a set of non orthonormal Bell states by adding discrete variables (Fock states) to the definition of the Bell-Cat states, which in the original definition carry only continuous variables (coherent states). We leave as perspectives the study of the viability of the use of this new set of states as building blocks of technologies which explore entanglement and teleportation protocols such as quantum repeater and quantum internet.(c) 2022 Elsevier Inc. All rights reserved.