About the nonclassicality of states defined by nonpositivity of theP-quasiprobability

Abstract

The definition of nonclassical states in quantum optics by the nonpositivity of their Glauber–Sudarshan quasiprobability is investigated and it is shown that it hides some serious problems. It leads to a subdivision of squeezed thermal states into classical and nonclassical states which is difficult to interpret physically by some qualitatively different behaviour of the states. Nonclassical states are found in arbitrarily small neighbourhoods of every classical state that is illustrated by a very artificial modified thermal state. The observability of the criterion in comparison to that for nonclassicality of states determined by the nearest Hilbert–Schmidt distance to a class of reference states is discussed. The behaviour of the nonclassicality of states in models of phase-insensitive processes of damping and amplification is investigated and it is found that every nonclassical state eventually makes a transition to a classical state. However, this is not specific for the negativities or singularities of the Glauber–Sudarshan quasiprobability and is found in similar form for other quasiprobabilities, for example, for the Wigner quasiprobability. We discuss in quite general form some defects of the Glauber–Sudarshan quasiprobability if compared with classical distribution functions over the phase space, in particular the failure of an earlier advertised superposition formula.