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Physical Review A

Comment on “Nonclassicality indicator for the real phase-space distribution functions”

Anatole Kenfack

Published Mar 16, 2016• 6 citations
Publisher

Abstract

We show in this Comment that the nonclassicality indicator proposed in Sadeghi et al. [Phys. Rev. A 82, 012102 (2010)] is controversial. Defined in terms of the interferences displayed by the quasidistribution function of at least two superposition states, this indicator may logically lead to zero for any single quantum state irrespective to its nonclassicality, in contradiction with their results.

DOI
10.1103/physreva.93.036101

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We show in this Comment that the nonclassicality indicator proposed in Sadeghi et al. [Phys. Rev. A 82, 012102 (2010)] is controversial. Defined in terms of the interferences displayed by the quasidistribution function of at least two superposition states, this indicator may logically lead to zero for any single quantum state irrespective to its nonclassicality, in contradiction with their results.
Sadeghi et al. [Phys. Rev. A 82, 012102 (2010)] presented a new nonclassicality indicator which works properly for Husimi and Rivier distribution functions as well as the Wigner distribution function. Some objections on the Sadeghi nonclassicality indicator are presented by Kenfack (preceding Comment, ``Nonclassicality indicator for the real phase-space distribution functions'', Phys. Rev. A 93, 036101 (2016). In this Reply, some misconceptions on Sadeghi's nonclassicality indicator are discussed and clarified.
Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schr\"odinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.
In this paper we define the quantum version of the Tsallis entropy in terms of quantum phase space distribution functions. The quantum Tsallis entropy is compared with Kenfack's nonclassicality indicator, for different systems, such as the Schr\"odinger cat state, the thermal state, a superposition of the ground and the first excited number states, and the harmonic oscillator state. These comparisons indicate that the Wigner representation gives us complete information about the state with the nonextensivity parameter q=1q=1q=1, while the Husimi representation hides some information with the nonextensivity parameter q<1q<1q<1.
We discuss a family of quasidistributions (sss-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schr\"odinger equation. It turns out that although Wigner functions satisfy the Schr\"odinger equation in phase space, they have a completely different interpretation.