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This article is cited in 8 scientific papers (total in 8 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.
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
Linking options:
https://www.mathnet.ru/eng/tmf8970https://doi.org/10.4213/tmf8970 https://www.mathnet.ru/eng/tmf/v186/i3/p401
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Abstract page: | 550 | Full-text PDF : | 180 | References: | 68 | First page: | 27 |
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