Abstract

An appropriate measure for the similarity of states in quantum theory is the distance of these states. To exclude some arbitrariness due to the unessential global U(l) phases of pure states, the distance of states has to be considered on the level of density operators which unites pure and mixed states. The distance of states based on the Hilbert-Schmidt norm of operators is best suited for explicit calculations that will be illustrated. The nearest distance of given states to a certain coherent state can be taken as a measure for the classicality of states [1]. We show that this measure is better correlated with an intuitive understanding of the classicality of states than, for example, the characterization by super-Poissonian and sub-Poissonian statistics. For pure states, the difference of the maximal height of the coherent-state quasiprobability Q(α,α^*) to its maximal possible value 1/π is proportional to this squared distance and can immediately be assessed from graphics of the coherent-state quasiprobability.

© 1998 IEEE