Classicality and anticlassicality measures of pure and mixed quantum states

We introduce a simple measure of classicality of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt scalar products between the renormalized statistical operators of the state concerned and all displaced thermal states. Choosing Fock states as the reference set, we introduce the measure of anticlassicality. Both measures are illustrated for the Fock, coherent phase, and generic mixed Gaussian states. Gaussian states are shown to be the closest to thermal states possessing the same degree of quantum purity. On the contrary, Fock states appear to be more close to mixed thermal states than to pure coherent states. (C) 2003 Elsevier Science B.V. All rights reserved.