A New Theorem on the Nonclassicality of States

A new theorem on the non-classicality depth of states has been proved. We show that if Wρ ̂ (αm, sm) = 0 exist for some value of the ordering parameter s at some phase-space point αm, and if Wρ ̂ (α, sm) is an ac-ceptable quasi-classical distribution, the non-classicality of ρ ̂ in parallel with Lee’s non-classicality depth is then given by τm = (1 − sm) /2. In this way, a general examination of the effects of the single-photon-addition and-subtraction operations has been studied. The theorem, indeed, pro-vides a theoretical background for generating quantum states of arbitrary non-classicality depth