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TMF, 2011, Volume 168, Number 1, Pages 151–161 (Mi tmf6670)  

This article is cited in 5 scientific papers (total in 5 papers)

Probability representation of spin states and inequalities for unitary matrices

M. A. Man'ko

Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: We review the probability representation of spin states described by probability distributions (tomograms). We use the relation of a tomogram to unitary group elements to obtain some inequalities for unitary matrices. We present the Cirel'son bound and the entropic inequalities for entangled spin states in the form of relations for functions on the unitary group.

Keywords: entanglement, tomographic probability, Bell's inequality, entropic uncertainty relation

DOI: https://doi.org/10.4213/tmf6670

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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 985–993

Bibliographic databases:


Citation: M. A. Man'ko, “Probability representation of spin states and inequalities for unitary matrices”, TMF, 168:1 (2011), 151–161; Theoret. and Math. Phys., 168:1 (2011), 985–993

Citation in format AMSBIB
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\paper Probability representation of spin states and inequalities for unitary matrices
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\pages 151--161
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Man'ko M.A. Man'ko V.I., “States in the Weyl–Wigner and tomographic-probability representations and entropic inequalities”, Phys. Scr., T147 (2012), 014020  crossref  adsnasa  isi  scopus
    2. Man'ko M.A. Man'ko V.I., “Statistics of observables in the probability representation of quantum and classical system states”, Foundations of Probability and Physics - 6, AIP Conf. Proc., 1424, ed. DAriano M. Fei S. Haven E. Hiesmayr B. Jaeger G. Khrennikov A. Larsson J., Amer. Inst. Physics, 2012  crossref  mathscinet  isi  scopus
    3. Man'ko M.A. Man'ko V.I., “Inequalities for Nonnegative Numbers and Information Properties of Qudit Tomograms”, J. Russ. Laser Res., 34:3 (2013), 203–218  crossref  isi  scopus
    4. Man'ko M.A., “Joint Probability Distributions and Conditional Probabilities in the Tomographic Representation of Quantum States”, Phys. Scr., T153 (2013), 014045  crossref  adsnasa  isi  scopus
    5. Fedorov A.K. Kiktenko E.O., “Quaternion Representation and Symplectic Spin Tomography”, J. Russ. Laser Res., 34:5 (2013), 477–487  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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