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

Bulletin of the Russian Academy of Sciences Physics

Tomographic representation of quantum mechanics and statistical physics

Olga V. Man’ko

Published May 1, 2008• 0 citations
Publisher

Abstract

The tomographic representation for operators dependent of continuous variables, as an example of star-product quantization, and the relationship between the tomographic representations of quantum mechanics and classical statistical mechanics are discussed.
DOI
10.3103/s1062873808050316

Related papers

Tomographic Representation of Quantum Mechanics and Statistical Physics

Olga V. Manko, Luigi Accardi, Guillaume Adenier +5 more

A review of the photon‐number tomography and symplectic tomography as examples of star‐product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.

arXiv:0902.4593•AIP conference proceedings•Jan 1, 2009•7 citations

Star-product quantization and symplectic tomography

Olga V. Man’ko

A review of the symplectic tomographic approaches within the framework of star-product quantization is presented. The classical statistical mechanics within the framework of the tomographic representation is considered. The kernels of the star product of functions–symbols of operators in classical and quantum mechanics, are presented.

arXiv:0902.4559•Physica Scripta•Jul 1, 2009•1 citation

Probability representation of quantum mechanics and star product quantization

S. N. Belolipetskiy, Vladimir N. Chernega, Olga V. Man’ko +1 more

The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in Hilbert space onto these functions is presented. Examples of the Wigner-Weyl symbols (like Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified with the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators which are needed to construct the bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relation of the structure constants of the associative star-product of the operator symbols to the quantizer-dequantizer operators is reviewed.

arXiv:1903.07932•Mar 19, 2019•0 citations

Probability representation of quantum mechanics and star product quantization

Vladimir N. Chernega, S. N. Belolipetskiy, Olga V. Man’ko +1 more

Abstract This paper presents a review of star-product formalism. This formalism provides a description for quantum states and observables by means of the functions called’ symbols of operators’. Those functions are obtained via bijective maps of the operators acting in Hilbert space. Examples of the Wigner-Weyl symbols (Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified for the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators required for construction of bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relationship between structure constants of associative star-product of operator symbols and quantizer-dequantizer operators is reviewed.

Journal of Physics Conference Series•Dec 1, 2019•9 citations

A tomographic approach to quantum nonlocality

Stefano Mancini, Vladimir I. Man’ko, Evgeny V Shchukin +1 more

We propose a tomographic approach to study quantum nonlocality in continuous variable quantum systems. On one hand we derive a Bell-like inequality for measured tomograms. On the other hand, we introduce pseudospin operators whose statistics can be inferred from the data characterizing the reconstructed state, thus giving the possibility to use standard Bell's inequalities. Illuminating examples are also discussed.

arXiv:quant-ph/0302089•Journal of Optics B Quantum and Semiclassical Optics•Jun 1, 2003•16 citations

Deformation quantization and the tomographic representation of quantum fields

Jasel Berra–Montiel, Roberto Cartas-Fuentevilla

The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.

arXiv:2006.07688•International Journal of Geometric Methods in Modern Physics•Oct 6, 2020•5 citations
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in Hilbert space onto these functions is presented. Examples of the Wigner-Weyl symbols (like Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified with the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators which are needed to construct the bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relation of the structure constants of the associative star-product of the operator symbols to the quantizer-dequantizer operators is reviewed.
Abstract This paper presents a review of star-product formalism. This formalism provides a description for quantum states and observables by means of the functions called’ symbols of operators’. Those functions are obtained via bijective maps of the operators acting in Hilbert space. Examples of the Wigner-Weyl symbols (Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified for the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators required for construction of bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relationship between structure constants of associative star-product of operator symbols and quantizer-dequantizer operators is reviewed.
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic version of the Wigner map allows us to compute the symbols corresponding to field operators. Finally, the functional integral representation of the tomographic star product is determined. Some possible applications of the formalism to loop quantum cosmology and loop quantum gravity are briefly discussed.