Sampling entropies and operational phase-space measurement. II. Detection of quantum coherences

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Abstract
We use the operational phase-space distributions and sampling entropies developed in the preceding paper [V. Bužek, C. H. Keitel, and P. L. Knight, Phys. Rev. A 51, 2575 (1995)] to discuss the nature of quantum interference between components of superpositions of states. We show how the Wehrl entropy, a special case of the sampling entropy, is a useful discriminator between different kinds of superpositions and of statistical mixtures, and is determined essentially by the coherent-state content. Apart from interference terms, this content is given by the quantum uncertainty of a single coherent state and the classical contribution to the number of coherent states necessary to tile the dominant phase-space ‘‘patch’’ representing the quantum state of interest. We illustrate these ideas using nonclassical superpositions of coherent states, where interference modifies the phase-space distributions, and show how these features are sensitive to dissipation.