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TMF, 1998, Volume 115, Number 2, Pages 185–198 (Mi tmf866)  

This article is cited in 19 scientific papers (total in 19 papers)

Describing spinors using probability distribution functions

V. I. Man'ko, O. V. Man'ko, S. S. Safonov

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: Irreducible representations of the rotation group are realized using a family of positive probability distributions of the spin projections for an arbitrary value of the spin. The family is parametrized by the points on the sphere. An invertible mapping of the spinors onto the probability distribution functions is constructed. Examples of probability distributions for the well-known states with the spins $1/2$ and $1$ are presented.

DOI: https://doi.org/10.4213/tmf866

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English version:
Theoretical and Mathematical Physics, 1998, 115:2, 520–529

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Received: 06.11.1997

Citation: V. I. Man'ko, O. V. Man'ko, S. S. Safonov, “Describing spinors using probability distribution functions”, TMF, 115:2 (1998), 185–198; Theoret. and Math. Phys., 115:2 (1998), 520–529

Citation in format AMSBIB
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\by V.~I.~Man'ko, O.~V.~Man'ko, S.~S.~Safonov
\paper Describing spinors using probability distribution functions
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\pages 185--198
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\jour Theoret. and Math. Phys.
\yr 1998
\vol 115
\issue 2
\pages 520--529
\crossref{https://doi.org/10.1007/BF02575452}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Andreev, VA, “Spin states and probability distribution functions”, Journal of Russian Laser Research, 19:4 (1998), 340  crossref  isi  scopus  scopus
    2. Andreev, VA, “Tomography of two-particle spin states”, Journal of Experimental and Theoretical Physics, 87:2 (1998), 239  crossref  adsnasa  isi  scopus  scopus
    3. Andreev, VA, “The classification of two-particle spin states and generalized Bell inequalities”, Physics Letters A, 281:5–6 (2001), 278  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Man'ko, O, “Photon-number tomography of multimode states and positivity of the density matrix”, Journal of Russian Laser Research, 24:5 (2003), 497  crossref  isi  scopus  scopus  scopus
    5. Castanos, O, “Kernel of star-product for spin tomograms”, Journal of Physics A-Mathematical and General, 36:16 (2003), 4677  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Man'ko O.V., “Photon-number tomogram for two-mode squeezed state”, Proceedings of the 8th International Conference on Squeezed States and Uncertainty Relations, 2003, 254–261  isi
    7. Man'ko, O, “Classical mechanics is not the h -> 0 limit of quantum mechanics”, Journal of Russian Laser Research, 25:5 (2004), 477  crossref  mathscinet  isi  scopus  scopus  scopus
    8. Man'ko, O, “Probability-representation entropy for spin-state tomogram”, Journal of Russian Laser Research, 25:2 (2004), 115  crossref  isi  scopus  scopus  scopus
    9. Man'ko, OV, “Probability representation of classical states”, Journal of Russian Laser Research, 26:6 (2005), 429  crossref  isi  scopus  scopus  scopus
    10. Lupo, C, “Bell's inequalities in the tomographic representation”, Journal of Physics A-Mathematical and General, 39:40 (2006), 12515  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. Man'ko, OV, “Probability representation and spin states of two particles”, Journal of Russian Laser Research, 27:4 (2006), 319  crossref  isi  scopus  scopus  scopus
    12. Filippov, SN, “Chebyshev polynomials and Fourier transform of SU(2) irreducible representation character as spin tomographic star-product kernel”, Journal of Russian Laser Research, 30:3 (2009), 224  crossref  isi  scopus  scopus
    13. Filippov, SN, “Spin tomography and star-product kernel for qubits and qutrits”, Journal of Russian Laser Research, 30:2 (2009), 129  crossref  isi  scopus  scopus  scopus
    14. Filippov S.N., Man'ko V.I., “Inverse Spin-S Portrait and Representation of Qudit States by Single Probability Vectors”, Journal of Russian Laser Research, 31:1 (2010), 32–54  crossref  isi  scopus  scopus
    15. Kiktenko E.O., Korotaev S.M., Fedorov A.K., Yurchenko S.O., “Prichinnyi analiz zaputannykh sostoyanii v tomograficheskom predstavlenii kvantovoi mekhaniki”, Vestnik moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. seriya: estestvennye nauki, 2012, 75–85  elib
    16. Fedorov A.K. Kiktenko E.O., “Quaternion Representation and Symplectic Spin Tomography”, J. Russ. Laser Res., 34:5 (2013), 477–487  crossref  isi  scopus  scopus
    17. Kiktenko E. Fedorov A., “Tomographic Causal Analysis of Two-Qubit States and Tomographic Discord”, Phys. Lett. A, 378:24-25 (2014), 1704–1710  crossref  mathscinet  zmath  isi  scopus  scopus
    18. Thapliyal K., Banerjee S., Pathak A., “Tomograms For Open Quantum Systems: in(Finite) Dimensional Optical and Spin Systems”, Ann. Phys., 366 (2016), 148–167  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    19. Chernega V.N., Man'ko O.V., Man'ko V.I., “Probability Representation of Quantum States as a Renaissance of Hidden Variables God Plays Coins”, J. Russ. Laser Res., 40:2 (2019), 107–120  crossref  isi
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