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arXiv:1511.02223

Non-classicality indicators for entangled and squeezed number states

Siamak Khademi, Elham Motaghi, Parvin Sadeghi

Published Nov 6, 2015• 0 citations
arXivHTMLPDF

Abstract

Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits with respect to the Kenfack's indicator. For the two-level entangled state, we show a correspondence between the Sadeghi's non-classicality indicator and the Von Neumann entropy. It is also shown that for the superposition of squeezed number state the Sadeghi's (and no Kenfack's) non-classicality indicators is sensible with respect to the squeezing parameter for a superposition of squeezed number states.

DOI
10.48550/arxiv.1511.02223

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Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits with respect to the Kenfack's indicator. For the two-level entangled state, we show a correspondence between the Sadeghi's non-classicality indicator and the Von Neumann entropy. It is also shown that for the superposition of squeezed number state the Sadeghi's (and no Kenfack's) non-classicality indicators is sensible with respect to the squeezing parameter for a superposition of squeezed number states.
Non-classicality indicators are widely applied to describe the physical properties of quantum states. One category of these indicators is defined in terms of negativities portion of Wigner distribution function. These indicators are not indicating to some quantum properties, e.g.: squeezing. Because the squeezing operations don’t effect on, the amount of negativities of Wigner distribution functions. Therefore the non-classicality indicators, e.g.: Kenfak or Benedict, which are working based on the negativities of distribution functions, cannot recognize the squeezing properties. In this paper a non-classicality indicator is introduced, in terms of the radial and angular distribution of absolute value of Wigner distribution function, which can recognize the squeezing properties, e.g.: squeezing parameter and squeezing angle. This non-classicality indicator is applied for the squeezed photonic states. We show that this indicator can evaluate the number of photons as well as the squeezing parameter and squeezing angle.
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.
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.
In this paper, a quantitative investigation of the non-classical and quantum non-Gaussian characters of the photon-subtracted displaced Fock state [Formula: see text], where k is the number of photons subtracted and n is Fock parameter, is performed by using a collection of measures like Wigner logarithmic negativity, linear entropy potential, skew information-based measure, and relative entropy of quantum non-Gaussianity. It is noticed that the number of photons subtracted ( k) changes the nonclassicality and quantum non-Gaussianity in a significant amount in the regime of small values of the displacement parameter, whereas the Fock parameter ( n) presents a notable change in the large regime of the displacement parameter. In this respect, the role of the Fock parameter is found to be stronger as compared to the photon subtraction number. Finally, the Wigner function dynamics considering the effects of photon loss channel is used to show that the Wigner negativity can only be detected by highly efficient detectors.