Classical and quantum-mechanical phase space distributions

Abstract

We examine the notion of nonclassicality in terms of quasiprobability distributions. In particular, we do not only ask if a specific quasiprobability can be interpreted as a classical probability density, but require that characteristic features of classical electrodynamics are resembled. We show that the only quasiprobabilities which correctly describe the superposition principle of classical electromagnetic fields are the $s$-parameterized quasiprobabilities. Furthermore, the Glauber-Sudarshan P function is the only quantum-mechanical quasiprobability which is transformed at a classical attenuator in the same way as a classical probability distribution. This result strengthens the definition of nonclassicality in terms of the P function, in contrast to possible definitions in terms of other quasiprobabilities.

7 pages, 3 figures

References in corpus (6)

• Experimental nonclassicality of single-photon-added thermal light states
• Directly estimating non-classicality
• Nonclassical correlation properties of radiation fields
• Probing the negative Wigner function of a pulsed single photon point by point
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Cited by in corpus (8)

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• Quantumness Beyond Entanglement: The Case of Symmetric States
• Hydrodynamic interpretation of generic squeezed coherent states: A kinetic theory
• Exploiting Spatial Diversity in Earth-to-Satellite Quantum-Classical Communications