RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2006, Volume 146, Number 1, Pages 172–185 (Mi tmf2017)  

This article is cited in 31 scientific papers (total in 31 papers)

Tomography of Spin States, the Entanglement Criterion, and Bell's Inequalities

V. A. Andreev, V. I. Man'ko, O. V. Man'ko, E. V. Shchukin

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

Abstract: We review the method of spin tomography of quantum states in which we use the standard probability distribution functions to describe spin projections on selected directions, which provides the same information about states as is obtained by the density matrix method. In this approach, we show that satisfaction or violation of Bell's inequalities can be understood as properties of tomographic functions for joint probability distributions for two spins. We compare results obtained using the methods of classical probability theory with those obtained in the framework of traditional quantum mechanics.

Keywords: quantum tomography, probability, distribution function, Bell's inequality

DOI: https://doi.org/10.4213/tmf2017

Full text: PDF file (185 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2006, 146:1, 140–151

Bibliographic databases:


Citation: V. A. Andreev, V. I. Man'ko, O. V. Man'ko, E. V. Shchukin, “Tomography of Spin States, the Entanglement Criterion, and Bell's Inequalities”, TMF, 146:1 (2006), 172–185; Theoret. and Math. Phys., 146:1 (2006), 140–151

Citation in format AMSBIB
\Bibitem{AndManMan06}
\by V.~A.~Andreev, V.~I.~Man'ko, O.~V.~Man'ko, E.~V.~Shchukin
\paper Tomography of Spin States, the Entanglement Criterion, and Bell's Inequalities
\jour TMF
\yr 2006
\vol 146
\issue 1
\pages 172--185
\mathnet{http://mi.mathnet.ru/tmf2017}
\crossref{https://doi.org/10.4213/tmf2017}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2243411}
\zmath{https://zbmath.org/?q=an:1177.81017}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2006TMP...146..140A}
\elib{http://elibrary.ru/item.asp?id=9213644}
\transl
\jour Theoret. and Math. Phys.
\yr 2006
\vol 146
\issue 1
\pages 140--151
\crossref{https://doi.org/10.1007/s11232-006-0014-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000235509200014}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-31044439117}


Linking options:
  • http://mi.mathnet.ru/eng/tmf2017
  • https://doi.org/10.4213/tmf2017
  • http://mi.mathnet.ru/eng/tmf/v146/i1/p172

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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 OV, Man'ko VI, “Probability representation and spin states of two particles”, Journal of Russian Laser Research, 27:4 (2006), 319–326  crossref  isi  scopus  scopus
    2. 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
    3. Chernega, VN, “Tomographic characteristics of spin states”, Journal of Russian Laser Research, 27:2 (2006), 132  crossref  mathscinet  isi  scopus  scopus
    4. Man'ko O.V., Man'ko V.I., “Tomographic entropy for spin systems”, 12th Central European Workshop on Quantum Optics, Journal of Physics Conference Series, 36, 2006, 137–148  crossref  isi  scopus  scopus
    5. V. A. Andreev, “Generalized Bell inequality and a method for its verification”, Theoret. and Math. Phys., 152:3 (2007), 1286–1298  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Man'ko OV, “Star-product; Symplectic and spin tomographies”, Journal of Russian Laser Research, 28:5 (2007), 483–488  crossref  isi  scopus  scopus
    7. Lupo C, Man'ko VI, Marmo G, “Qubit portraits of qudit states and quantum correlations”, Journal of Physics A-Mathematical and Theoretical, 40:43 (2007), 13091–13100  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Khrennikov A, “Analysis of explicit and implicit assumptions in the theorems of J. Von Neumann and J. Bell”, Journal of Russian Laser Research, 28:3 (2007), 244–254  crossref  isi  scopus  scopus
    9. Man'ko VI, Shchekin AA, “Stochastic matrices generated by entangled states of qubit-qutrit systems”, Journal of Russian Laser Research, 28:3 (2007), 255–266  crossref  mathscinet  isi  scopus  scopus
    10. Chernega VN, Man'ko VI, “Qubit portrait of qudit states and Bell inequalities”, Journal of Russian Laser Research, 28:2 (2007), 103–124  crossref  isi  scopus  scopus
    11. Khrennikov A., “Bell's inequality: Nonlocalty, “Death of Reality”, or incompatibility of random variables?”, Quantum Theory: Reconsideration of Foundations - 4, AIP Conference Proceedings, 962, 2007, 121–131  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Man'ko V.I., “Probability instead of wave function and Bell inequalities as entanglement criterion”, Quantum Theory: Reconsideration of Foundations - 4, AIP Conference Proceedings, 962, 2007, 140–147  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. A. Yu. Khrennikov, “EPR–Bohm experiment and Bell's inequality: Quantum physics meets probability theory”, Theoret. and Math. Phys., 157:1 (2008), 1448–1460  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. Anisimov MA, Man'ko VI, “Wigner function and Bell's inequalities for even and odd coherent states”, Journal of Russian Laser Research, 29:3 (2008), 237–244  crossref  isi  scopus  scopus
    15. Khrennikov A, “Einstein-Podolsky-Rosen paradox, Bell's inequality, and the projection postulate”, Journal of Russian Laser Research, 29:2 (2008), 101–113  crossref  isi  scopus  scopus
    16. Adenier G, “A Fair Sampling Test for Epr-Bell Experiments”, Journal of Russian Laser Research, 29:5 (2008), 409–417  crossref  isi  scopus  scopus
    17. Man'ko V.I., “Semigroups of tomographic probabilities and quantum correlations”, 5th International Symposium on Quantum Theory and Symmetries QTS5, Journal of Physics Conference Series, 128, 2008  isi
    18. Anisimov, MA, “Probability distribution and Bell's inequality for the quantum qubit state”, Bulletin of the Lebedev Physics Institute, 36:4 (2009), 104  crossref  mathscinet  adsnasa  isi  scopus  scopus
    19. Filippov, SN, “Quantumness tests and witnesses in the tomographic-probability representation”, Physica Scripta, 79:5 (2009), 055007  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    20. Filippov, SN, “Qubit portrait of the photon-number tomogram and separability of two-mode light states”, Journal of Russian Laser Research, 30:1 (2009), 55  crossref  isi  scopus  scopus
    21. Akopyan, LV, “Bell-type inequalities in classical probability theory”, Journal of Russian Laser Research, 30:1 (2009), 82  crossref  mathscinet  isi  scopus  scopus
    22. Khrennikov, A, “Nonlocality as well as rejection of realism are only sufficient (but non-necessary!) conditions for violation of Bell's inequality”, Information Sciences, 179:5 (2009), 492  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    23. Andreev, VA, “Tomographic Probability Representation for Quantum Fermion Fields”, Journal of Russian Laser Research, 30:6 (2009), 591  crossref  isi  scopus  scopus
    24. Akopyan, LV, “Bell-Type Inequalities and Upper Bounds for Multiqudit States”, Journal of Russian Laser Research, 30:4 (2009), 338  crossref  isi  scopus  scopus
    25. Nikitin N.V., Toms K.S., “Relativistic Generalization of Bell's Inequalities in Wigner's Form”, Phys Atomic Nuclei, 72:12 (2009), 2027–2038  crossref  adsnasa  isi  elib  scopus  scopus
    26. M. A. Man'ko, “Probability representation of spin states and inequalities for unitary matrices”, Theoret. and Math. Phys., 168:1 (2011), 985–993  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    27. Akopyan L.V., Man'ko V.I., “General Bell-CHSH type and entropic inequalities based on quantum tomograms”, Optics and Spectroscopy, 111:4 (2011), 656–665  crossref  adsnasa  isi  scopus  scopus
    28. 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
    29. Man'ko O.V., “Photon-Number Tomography and Fidelity”, Quantum Theory: Reconsideration of Foundations 6, AIP Conference Proceedings, 1508, eds. Khrennikov A., Atmanspacher H., Migdall A., Polyakov S., Amer Inst Physics, 2012, 275–284  crossref  adsnasa  isi  scopus  scopus
    30. Fedorov A.K., Yurchenko S.O., “Quantum Tomograms and their Application in Quantum Information Science”, 21st International Laser Physics Workshop, Journal of Physics Conference Series, 414, IOP Publishing Ltd, 2013, 012040  crossref  isi  scopus  scopus
    31. Nikitin N.V., Sotnikov V.P., Toms K.S., “Time-Dependent Bell Inequalities in a Wigner Form”, Mosc. Univ. Phys. Bull., 69:6 (2014), 480–487  crossref  mathscinet  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:814
    Full text:272
    References:68
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019