Classicality and anticlassicality measures of pure and mixed quantum states

Dodonov, V. V.; Renó, M.B.

doi:10.1016/s0375-9601(03)00066-5

Cited by 47 publications

(41 citation statements)

References 63 publications

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“…It is worth noting that we are analyzing nonclassicality criteria but not a degree of nonclassicality. We admit that the latter problem is experimentally important and a few "measures" of nonclassicality have been proposed [49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

et al. 2010

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We consider a way to generate operational inequalities to test nonclassicality (or quantumness) of multimode bosonic fields (or multiparty bosonic systems) that unifies the derivation of many known inequalities and allows to propose new ones. The nonclassicality criteria are based on Vogel's criterion corresponding to analyzing the positivity of multimode P functions or, equivalently, the positivity of matrices of expectation values of, e.g., creation and annihilation operators. We analyze not only monomials but also polynomial functions of such moments, which can sometimes enable simpler derivations of physically relevant inequalities. As an example, we derive various classical inequalities which can be violated only by nonclassical fields. In particular, we show how the criteria introduced here easily reduce to the well-known inequalities describing (a) multimode quadrature squeezing and its generalizations, including sum, difference, and principal squeezing; (b) two-mode one-time photon-number correlations, including sub-Poisson photon-number correlations and effects corresponding to violations of the Cauchy-Schwarz and Muirhead inequalities; (c) two-time single-mode photon-number correlations, including photon antibunching and hyperbunching; and (d) two-and three-mode quantum entanglement. Other simple inequalities for testing nonclassicality are also proposed. We have found some general relations between the nonclassicality and entanglement criteria, in particular those resulting from the Cauchy-Schwarz inequality. It is shown that some known entanglement inequalities can be derived as nonclassicality inequalities within our formalism, while some other known entanglement inequalities can be seen as sums of more than one inequality derived from the nonclassicality criterion. This approach enables a deeper analysis of the entanglement for a given nonclassicality.

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Section: Introductionmentioning

confidence: 99%

Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

et al. 2010

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“…15,17,18,50,51 However, in our opinion, most of the existing indicators seem to be not fully satisfactory measures if one requires from them to be additive measures. The superscript "noncl" in notation S noncl is a shortening for the notion "nonclassicality," and the occurrence of the latter calls for elucidation.…”

Section: A Main Definitions and Relationsmentioning

confidence: 92%

Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems

Luzanov

2008

The Journal of Chemical Physics

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The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK(+) (for coordinate variables) and K(+)K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

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“…the Mandel's Q parameter [6]. Various criteria have been used in the literature in order to quantify the non-classical character of a given quantum state [6]. One such a criterion was introduced by Mandel [7], defining the parameter…”

Section: General Considerationsmentioning

confidence: 99%

“…For the canonical coherent states of the one-dimensional harmonic oscillator (HO-1D) [6] this deviation is zero and, consequently, the distribution function of these coherent states is Poissonian.…”

Section: General Considerationsmentioning

confidence: 99%

Generalized Barut-Girardello Coherent States for Mixed States with Arbitrary Distribution

et al. 2010

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In the paper we examine some properties of the generalized coherent states of the Barut-Girardello kind. These states are defined as eigenstates of a generalized lowering operator and they are strongly dependent on the structure constants. Besides the pure coherent states we focused our attention on the mixed states one, which are characterized by different probability distributions. As some examples we consider the thermal canonical distribution and the Poisson distribution functions. We calculate for these cases the Husimi's Q and quasi-probability P -distribution functions.

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Classicality and anticlassicality measures of pure and mixed quantum states

Cited by 47 publications

References 63 publications

Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

Testing nonclassicality in multimode fields: A unified derivation of classical inequalities

Spectral and entropic characterizations of Wigner functions: Applications to model vibrational systems

Generalized Barut-Girardello Coherent States for Mixed States with Arbitrary Distribution

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