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TMF, 2016, Volume 186, Number 3, Pages 401–422 (Mi tmf8970)  

This article is cited in 3 scientific papers (total in 3 papers)

Star product, discrete Wigner functions, and spin-system tomograms

P. Adama, V. A. Andreevb, A. Isarc, V. I. Man'kob, M. A. Man'kob

a Institute for Solid State Physics and Optics, Wigner Research Centre for Physics o  the H. A. S., Budapest, Hungary
b Lebedev Physical Institute, RAS, Moscow, Russia
c Horia Hulubei National Institute of Physics and Nuclear Engineering, Magurele, Romania

Abstract: We develop the star-product formalism for spin states and consider different methods for constructing operator systems forming sets of dequantizers and quantizers, establishing a relation between them. We study the physical meaning of the operator symbols related to them. Quantum tomograms can also serve as operator symbols. We show that the possibility to express discrete Wigner functions in terms of measurable quantities follows because these functions can be related to quantum tomograms. We investigate the physical meaning of tomograms and spin-system tomogram symbols, which they acquire in the framework of the star-product formalism. We study the structure of the sum kernels, which can be used to express the operator symbols, calculated using different sets of dequantizers and also arising in calculating the star product of operator symbols, in terms of one another.

Keywords: star product, quantizer, dequantizer, discrete Wigner function, kernel, fidelity, purity parameter

Funding Agency Grant Number
Hungarian Scientific Research Fund (OTKA) K83858
The research of V. A. Andreev, V. I. Man'ko, and M. A. Man'ko was supported by the Hungarian Scientific Research Fund (OTKA Contract No. K83858). The research of A. Isar was supported the Ministry of Education and Scientific Research, Romania (Project No. CNCS-UEFISCDI PN-II-ID-PCE-2011-3-0083).}


DOI: https://doi.org/10.4213/tmf8970

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English version:
Theoretical and Mathematical Physics, 2016, 186:3, 346–364

Bibliographic databases:

Received: 28.05.2015
Revised: 18.06.2015

Citation: P. Adam, V. A. Andreev, A. Isar, V. I. Man'ko, M. A. Man'ko, “Star product, discrete Wigner functions, and spin-system tomograms”, TMF, 186:3 (2016), 401–422; Theoret. and Math. Phys., 186:3 (2016), 346–364

Citation in format AMSBIB
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\pages 401--422
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    This publication is cited in the following articles:
    1. P. Adam, V. A. Andreev, A. Isar, M. A. Man'ko, V. I. Man'ko, “Continuous sets of dequantizers and quantizers for one-qubit states*”, J. Russ. Laser Res., 37:6 (2016), 544–555  crossref  isi  scopus
    2. P. Adam, V. A. Andreev, A. Isar, M. A. Man'ko, V. I. Man'ko, “Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems”, Phys. Lett. A, 381:34 (2017), 2778–2782  crossref  mathscinet  zmath  isi  scopus
    3. P. Adam, V. A. Andreev, M. A. Man'ko, I V. Man'ko, “Symbols of multiqubit states admitting a physical interpretation”, J. Russ. Laser Res., 39:4 (2018), 360–375  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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