SAMPLING ENTROPIES AND OPERATIONAL PHASE-SPACE MEASUREMENT .1. GENERAL FORMALISM

We present an entropic description of quantum-mechanical states based on an operational approach to a phase-space measurement. We give a simple phase-space interpretation of sampling entropies in terms of which we derive very general entropic uncertainty relations reflecting the degree of the phase-space uncertainty of the quantum-mechanical state in the given measurement (i.e., for a given ''quantum-ruler'' state). We relate the sampling entropy to the von Neumann and Shannon entropy and show that the Wehrl entropy represents a particular example of a sampling entropy when the quantum ruler is represented by coherent states. © 1995 The American Physical Society.