On Families of Wigner Functions for N-Level Quantum Systems

Abgaryan, Vahagn; Khvedelidze, A.

doi:10.3390/sym13061013

Cited by 7 publications

(11 citation statements)

References 27 publications

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“…We expect that this parameterization will be useful from a computational point of view in many physical applications including the models of elementary particles. Particularly, in forthcoming publications it will be used for the evaluation of very recently introduced indicators of quantumness/classicality of quantum states which are based on the potential of the Wigner quasidistributions to attain negative values [35]- [37].…”

Section: Discussionmentioning

confidence: 99%

Parameterizing qudit states

Khvedelidze

Mladenov²,

Torosyan

2021

Discrete and Continuous Models

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Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

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Section: Discussionmentioning

confidence: 99%

Parameterizing qudit states

Khvedelidze

Mladenov²,

Torosyan

2021

Discrete and Continuous Models

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“…It has been shown [7] that for N -level quantum system the Stratonovich-Weyl correspondence clauses admit simple formulation in the form of algebraic equations on spectrum of SW kernel:…”

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

confidence: 99%

“…parameterising the moduli space of solutions to (7). Hereafter, dealing with the Wigner function of density matrix ρ we will point at this ambiguity by explicitly writing dependence of SW kernel on the moduli space parameters ν:…”

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

confidence: 99%

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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 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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“…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%

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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On Families of Wigner Functions for N-Level Quantum Systems

Cited by 7 publications

References 27 publications

Parameterizing qudit states

Parameterizing qudit states

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

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