### 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.

Original language | English |
---|---|

Pages (from-to) | 346-364 |

Number of pages | 19 |

Journal | Theoretical and Mathematical Physics |

Volume | 186 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 1 2016 |

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### Keywords

- dequantizer
- discrete Wigner function
- fidelity
- kernel
- purity parameter
- quantizer
- star product

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Theoretical and Mathematical Physics*,

*186*(3), 346-364. https://doi.org/10.1134/S0040577916030041

**Star product, discrete Wigner functions, and spin-system tomograms.** / Ádám, P.; Andreev, V. A.; Isar, A.; Man’ko, V. I.; Man’ko, M. A.

Research output: Contribution to journal › Article

*Theoretical and Mathematical Physics*, vol. 186, no. 3, pp. 346-364. https://doi.org/10.1134/S0040577916030041

}

TY - JOUR

T1 - Star product, discrete Wigner functions, and spin-system tomograms

AU - Ádám, P.

AU - Andreev, V. A.

AU - Isar, A.

AU - Man’ko, V. I.

AU - Man’ko, M. A.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - dequantizer

KW - discrete Wigner function

KW - fidelity

KW - kernel

KW - purity parameter

KW - quantizer

KW - star product

UR - http://www.scopus.com/inward/record.url?scp=84962702616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962702616&partnerID=8YFLogxK

U2 - 10.1134/S0040577916030041

DO - 10.1134/S0040577916030041

M3 - Article

AN - SCOPUS:84962702616

VL - 186

SP - 346

EP - 364

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

SN - 0040-5779

IS - 3

ER -