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Bernstein’s paradox of entangled quantum states

 a, b,  a, b
a Lomonosov Moscow State University, Department of Physics, Vorobevy gory, Moscow, 119992, Russian Federation
b International Laser Center of M.V. Lomonosov Moscow State University, Vorobevy gory, Moscow, 119992, Russian Federation

Bernstein’s classical paradox of right colored-faced tetrahedron, while designed to illustrate the subtleties of probability theory, is strongly flawed in being asymmetric: three of the tetrahedron’s faces are single- and one, is multi-colored. Therefore, even prior to formal calculations, a strong suspicion as to the independence of outcoming statistics arises. Not so with entangled states. In the schematic solutions proposed, while photon detection channels are completely symmetric and equivalent, the events that occur in them turn out to be statistically dependent, making the Bernstein paradox even more impressive due to the unusual behavior of quantum particles not obeying classical laws. As an illustrative example of the probability paradox, Greenberger—Horne—Zeilinger multiqubit states are considered.

Text can be downloaded in Russian. English translation is available here.
PACS: 03.65.Ud, 42.65.Lm (all)
DOI: 10.3367/UFNe.0183.201311e.1231
URL: https://ufn.ru/en/articles/2013/11/d/
Citation: Belinskii A V, Chirkin A S "Bernstein's paradox of entangled quantum states" Phys. Usp. 56 1126–1131 (2013)
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Received: 22nd, April 2013, revised: 13th, June 2013, 30th, May 2013

Оригинал: Белинский А В, Чиркин А С «Парадокс Бернштейна с запутанными квантовыми состояниями» УФН 183 1231–1236 (2013); DOI: 10.3367/UFNr.0183.201311e.1231

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  1. A.V. Belinsky, M.Kh. Shulman “Quantum nature of a nonlinear beam splitter57 1022–1034 (2014)
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  3. A.M. Zheltikov “The critique of quantum mind: measurement, consciousness, delayed choice, and lost coherence61 1016–1025 (2018)
  4. A.V. Belinskii “Bell’s theorem for trichotomic observables40 305–316 (1997)
  5. D.N. Klyshko “The Einstein-Podolsky-Rosen paradox for energy-time variables32 555–563 (1989)
  6. A.V. Belinskii “Bell’s theorem without the hypothesis of locality37 219–222 (1994)
  7. B.B. Kadomtsev “Irreversibility in quantum mechanics46 1183–1201 (2003)
  8. D.N. Klyshko “A simple method of preparing pure states of an optical field, of implementing the Einstein-Podolsky-Rosen experiment, and of demonstrating the complementarity principle31 74–85 (1988)
  9. V.V. Mityugov “The tree of paradox36 (8) 744–753 (1993)
  10. V.P. Demutskii, R.V. Polovin “Conceptual problems in quantum mechanics35 (10) 857–896 (1992)
  11. M.B. Mensky “Measurability of quantum fields and the energy—time uncertainty relation54 519–528 (2011)
  12. B.B. Kadomtsev “Classical and quantum irreversibility38 923–929 (1995)
  13. A.V. Belinskii “Bell’s paradoxes without the introduction of hidden variables37 413–419 (1994)
  14. A.A. Grib “On the problem of the interpretation of quantum physics56 1230–1244 (2013)
  15. A.V. Belinskii “Regular and quasiregular spectra of disordered layer structures38 653–664 (1995)
  16. A.V. Belinsky “About David Bohm "wave-pilot" concept”, accepted

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