Comment on “Nonclassical depth of the phase state”

Marcelo A. Marchiolli, Vanderlei Salvador Bagnato, Y. Guimarães +1 more

Anatole Kenfack

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.

J. M. C. Malbouisson, B. Baseia

The degree of nonclassicality of states of a field mode is analysed considering both phase-space and distance-type measures of nonclassicality. By working out some general examples, it is shown explicitly that the phase-space measure is rather sensitive to superposition of states, with finite superpositions possessing maximum nonclassical depth (the highest degree of nonclassicality) irrespective of the nature of the component states. Mixed states are also discussed and examples with nonclassical depth varying between the minimum and the maximum allowed values are exhibited. For pure Gaussian states, it is demonstrated that distance-type measures based on the Hilbert–Schmidt metric are equivalent to the phase-space measure. Analyzing some examples, it is shown that distance-type measures are efficient to quantify the degree of nonclassicality of non-Gaussian pure states.

Y. Guimarães, B. Baseia, Celso J. Villas-Bôas +1 more

Siamak Khademi, Parvin Sadeghi, S. Nasiri

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.

Timothy H. Boyer