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ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА

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

A. Khvedelidze, I. Rogojin, I. Rogozhin

Published Sep 24, 2025• 0 citations
OpenAlex

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.

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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.
There are different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g., to perform full tomography of this state. For instance, quasi-distributions such as the Weyl or Wigner distributions provide complete information about a quantum state which is equivalent to the information contained in the density matrix. In the case of composite systems, of which the subsystems are not necessarily located at the same place, the experimental feasibility of the tomographic process is considerably simplified whenever it can be realized through local operations and classical communications between local observers. This brings us naturally to study the possibility to factorize the (discrete) Wigner distribution of a composite system into the product of local Wigner distributions, which is the subject of the present paper. The discrete Heisenberg-Weyl group is an essential ingredient of our approach.
As is well known, there are several formulations of quantum mechanics. One of them, closely connected with the Weyl representation of operators [ 1 ] and Wigner functions [ 2 ], use functions on the phase space to represent both observables and quantum states. For working in this representation it is necessary to replace operators by their Weyl symbols and density matrices by Wigner functions [ 3 , 4 ]. After fundamental works of Weyl, Wigner and Kirkwood [ 1 , 2 , 5 ] properties of the representation were studied and used to calculate the properties of various physical systems (see [ 6–23 ]), including systems with magnetic field [ 15–23 ].