Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of Particles and Nuclei

On the Dichotomy between Quatrits and Pairs of Qubits in the Stratonovich-Weyl Correspondence

A. Khvedelidze, I. Rogozhin

Published Aug 1, 2025• 0 citations
Publisher

Abstract

Abstract The issue of the dichotomy between the elementary and composite nature of a finite-dimensional quantum system is discussed within the framework of the generalized Stratonovich–Weyl formulation of quantum mechanics. Performing numerical studies, we demonstrate how information on the possibility of realizing a virtual 2-level subsystem is encoded in the properties of the Wigner function of a total 4-level system.

DOI
10.1134/s1063779625700145

Related papers

О дихотомии между кватритом и парой кубитов в соответствии Стратоновича–Вейля: Аннотации

A. Khvedelidze, I. Rogojin, I. Rogozhin

The issue of the dichotomy between the elementary and composite nature of a finite-dimensional quantum system is discussed within the framework of the generalized Stratonovich–Weyl formulation of quantum mechanics. Performing numerical studies, we demonstrate how information on the possibility of realizing a virtual 2-level subsystem is encoded in the properties of the Wigner function of a total 4-level system.

ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА•Sep 24, 2025•0 citations

Generalizing Stratonovich–Weyl Axioms for Composite Systems

A. Khvedelidze

Abstract The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich–Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.

arXiv:2209.13298•Physics of Particles and Nuclei•Nov 29, 2023•1 citation

On the family of Wigner functions for N-level quantum system

A. Khvedelidze, Vahagn Abgaryan

The family of unitary non-equivalent Weyl-Stratonovich kernels determining the Wigner probability distribution function of an arbitrary N-level quantum system is constructed.

arXiv:1708.05981•Aug 20, 2017•3 citations

Mathematical Aspects of the Weyl Correspondence

James C. T. Pool

The Weyl correspondence between classical and quantum observables is rigorously formulated for a linear mechanical system with a finite number of degrees of freedom. A multiplication of functions and a *-operation are introduced to make the Hilbert space of Lebesgue square-integrable complex-valued functions on phase space into a H*-algebra. The Weyl correspondence is realized as a *-isomorphism f → W(f) of this H*-algebra onto the H*-algebra of Hilbert-Schmidt operators on the Hilbert space of Lebesgue square-integrable complex-valued functions on configuration space. Moreover, the kernel of W(f) is exhibited in terms of a Fourier-Plancherel transform of f. Elementary properties of the Wigner quasiprobability density function and its characteristic function are deduced and used to obtain these results.

Journal of Mathematical Physics•Jan 1, 1966•203 citations

An elementary aspect of the Weyl‐Wigner representation

Joachim Dahl, Wolfgang P. Schleich

Abstract It is an elementary aspect of the Weyl‐Wigner representation of quantum mechanics that the dynamical phase‐space function corresponding to the square of a quantum‐mechanical operator is, in general, different from the square of the function representing the operator itself. We call attention to some conceptual consequences of this fact.

Fortschritte der Physik•Feb 26, 2003•2 citations

Об обобщении аксиом Стратоновича–Вейля для составных систем: Аннотации

A. Khvedelidze

The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich–Weyl axioms. Arguments are given in favour of a certain extension of the axioms, provided that there is a priori knowledge about the composite nature of the quantum system.

ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА•May 31, 2024•0 citations
Abstract The issue of the dichotomy between the elementary and composite nature of a finite-dimensional quantum system is discussed within the framework of the generalized Stratonovich–Weyl formulation of quantum mechanics. Performing numerical studies, we demonstrate how information on the possibility of realizing a virtual 2-level subsystem is encoded in the properties of the Wigner function of a total 4-level system.
The Weyl correspondence between classical and quantum observables is rigorously formulated for a linear mechanical system with a finite number of degrees of freedom. A multiplication of functions and a *-operation are introduced to make the Hilbert space of Lebesgue square-integrable complex-valued functions on phase space into a H*-algebra. The Weyl correspondence is realized as a *-isomorphism f → W(f) of this H*-algebra onto the H*-algebra of Hilbert-Schmidt operators on the Hilbert space of Lebesgue square-integrable complex-valued functions on configuration space. Moreover, the kernel of W(f) is exhibited in terms of a Fourier-Plancherel transform of f. Elementary properties of the Wigner quasiprobability density function and its characteristic function are deduced and used to obtain these results.