On the Moduli Space of Wigner Quasiprobability Distributions for N-Dimensional Quantum Systems

In this report we are aiming at introducing a global measure of non-classicality of the state space of N -level quantum systems and estimating it in the limit of large N . For this purpose we employ the Wigner function negativity as a non-classicality criteria. Thus, the specific volume of the support of negative values of Wigner function is treated as a measure of non-classicality of an individual state. Assuming that the states of an N -level quantum system are distributed by Hilbert-Schmidt measure (Hilbert-Schmidt ensemble), we define the global measure as the average non-classicality of the individual states over the Hilbert-Schmidt ensemble. We present the numerical estimate of this quantity as a result of random generation of states, and prove a proposition claiming its exact value in the limit of N → ∞.

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“…See more on the moduli space of parameters in [8].…”

Section: The Wigner Function Of a Density Operator Of N -Level Systemmentioning

confidence: 99%

“…Proof. Indeed, let us write down the volume integral (18) over negativity domain via the Heaviside step function θ[−W ν ρ (ω)] and use SVD decomposition (8) for SW kernel ∆(ω|ν) of the Wigner function…”

Section: Measures Of Non-classicality Of State and Overall Quantum Systemmentioning

confidence: 99%

On Overall Measure of Non-classicality of N-level Quantum System and Its Universality in the Large N Limit

Abgaryan

Khvedelidze

Rogojin

2020

Distributed Computer and Communication Networks

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“…In the present report we will discuss both issues, (I) and (II), constructing a classicality/quantumness measure for a family of the Wigner quasiprobability representation of finite-dimensional quantum systems. We will follow approach [9,10,11] to the construction of the Wigner quasiprobability distributions W (ν) (Ω N ) of an N −level quantum system via the dual pairing,…”

Section: Background and Motivationmentioning

confidence: 99%

“…. , ν s ), s ≤ N − 2 will be used to enumerate the Wigner distributions (see details in [10], [11]).…”

Section: Background and Motivationmentioning

confidence: 99%

On Measures of Classicality/Quantumness in Quasiprobability Representations of Finite-Dimensional Quantum Systems

Abbasli

Abgaryan

Bureš³

et al. 2020

Phys. Part. Nuclei

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In the present report we discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions. Particularly, the dependence of the global indicator of classicality on the assigned geometry of a quantum state space is analysed for a whole family of Wigner quasiprobability representations. General considerations are exemplified by constructing the global indicator of classicality/quantumness for the Hilbert-Schmidt, Bures and Bogoliubov-Kubo-Mori ensembles of qubits and qutrits.

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“…1 In the present note, we will focus on the problem of quantifying the nonclassicality of quantum systems associated with a finite-dimensional Hilbert space by studying the non-positivity of the Wigner quasiprobability distributions (the Wigner function, or shortly WF) [6,7,8,9]. Our treatment is based on the recent publications [10,11], where the Wigner quasiprobability distribution W (ν) (Ω N ) of an N −level quantum system is constructed via the dual pairing,…”

Section: Introductionmentioning

confidence: 99%

The global indicator of classicality of an arbitrary $N$-level quantum system

Abgaryan¹,

Khvedelidze²,

Torosyan³

2019

Preprint

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It is commonly accepted that a deviation of the Wigner quasiprobability distribution of a quantum state from a proper statistical distribution signifies its nonclassicality. Following this ideology, we introduce the global indicator Q N for quantification of "classicality-quantumness" correspondence in the form of the functional on the orbit space O[P N ] of the SU (N ) group adjoint action on the state space P N of an N -dimensional quantum system. The indicator Q N is defined as a relative volume of a subspace, where the Wigner quasiprobability distribution is positive. An algebraic structure of O[P (+) N ] is revealed and exemplified by a single qubit (N = 2) and single qutrit (N = 3). For the Hilbert-Schmidt ensemble of qutrits the dependence of global indicator on the moduli parameter of the Wigner quasiprobability distribution has been found.

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On the Moduli Space of Wigner Quasiprobability Distributions for N-Dimensional Quantum Systems

Cited by 4 publications

References 27 publications

On Overall Measure of Non-classicality of N-level Quantum System and Its Universality in the Large N Limit

On Overall Measure of Non-classicality of N-level Quantum System and Its Universality in the Large N Limit

On Measures of Classicality/Quantumness in Quasiprobability Representations of Finite-Dimensional Quantum Systems

The global indicator of classicality of an arbitrary $N$-level quantum system

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