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Bernstein’s paradox of entangled quantum states

 a, b,  a, b
a Lomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, 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.

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Fulltext is also available at DOI: 10.3367/UFNe.0183.201311e.1231
PACS: 03.65.Ud, 42.65.Lm (all)
DOI: 10.3367/UFNe.0183.201311e.1231
URL: https://ufn.ru/en/articles/2013/11/d/
000331111800004
2-s2.0-84893841610
2013PhyU...56.1126B
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

References (41) ↓ Cited by (3) Similar articles (20)

  1. Mandel’shtam L I Lektsii Po Optike, Teorii Otnositel’nosti i Kvantovoi Mekhanike (M.: Nauka, 1972)
  2. Einstein A, Podolsky B, Rosen N Phys. Rev. 47 777 (1935)
  3. Fok V A, Einshtein A, Podol’skii B, Rozen N, Bor N Usp. Fiz. Nauk 16 436 (1936)
  4. Bohr N Phys. Rev. 48 696 (1935)
  5. Klyshko D N Usp. Fiz. Nauk 154 133 (1988); Klyshko D N Sov. Phys. Usp. 31 74 (1988)
  6. Klyshko D N Usp. Fiz. Nauk 158 327 (1989); Klyshko D N Sov. Phys. Usp. 32 555 (1989)
  7. Kadomtsev B B Usp. Fiz. Nauk 164 449 (1994); Kadomtsev B B Phys. Usp. 37 425 (1994)
  8. Kadomtsev B B Usp. Fiz. Nauk 173 1221 (2003); Kadomtsev B B Phys. Usp. 46 1183 (2003)
  9. Reid M D et al. Rev. Mod. Phys. 81 1727 (2009)
  10. Bell J S Physics 1 195 (1964)
  11. Greenberger D M, Horne M, Zeilinger A Bell’s Theorem, Quantum Theory And Conceptions Of The Universe (Fundamental Theories of Physics) Vol. 37 (Ed. M Kafatos) (Dordrecht: Kluwer Acad., 1989) p. 69
  12. Greenberger D M, Horne M A, Zeilinger A Phys. Today 46 (8) 22 (1993)
  13. Pan J-W et al. Rev. Mod. Phys. 84 777 (2012)
  14. Clauser J F et al. Phys. Rev. Lett. 23 880 (1969)
  15. Mermin N D Phys. Rev. Lett. 65 1838 (1990)
  16. Ardehali M Phys. Rev. A 46 5375 (1992)
  17. Belinskii A V, Klyshko D N Usp. Fiz. Nauk 163 (8) 1 (1993); Belinskii A V, Klyshko D N Phys. Usp. 36 653 (1993)
  18. Brunner N, Sharam J, Vértesi T Phys. Rev. Lett. 108 110501 (2012)
  19. Lee S, Lee J, Kim J Phys. Rev. A 79 032309 (2009)
  20. Belinskii A V Usp. Fiz. Nauk 167 323 (1997); Belinskii A V Phys. Usp. 40 305 (1997)
  21. Belinskii A V Usp. Fiz. Nauk 173 905 (2003); Belinskii A V Phys. Usp. 46 877 (2003)
  22. Belinskii A V, Granovskii A A Pis’ma ZhETF 93 552 (2011); Belinsky A V, Granovskiy A A JETP Lett. 93 495 (2011)
  23. Menskii M B Usp. Fiz. Nauk 168 1017 (1998); Menskii M B Phys. Usp. 41 923 (1998)
  24. Menskii M B Usp. Fiz. Nauk 181 543 (2011); Mensky M B Phys. Usp. 54 519 (2011)
  25. Mensky M B Quantum Measurements And Decoherence. Models And Phenomenology (Dordrecht: Kluwer Acad. Publ., 2000); Menskii M B Kvantovye Izmereniya i Dekogerentsiya. Modeli i Fenomenologiya (M.: Fizmatlit, 2001)
  26. Facchi P, Pascazio S "Quantum Zeno and inverse quantum Zeno effects" Prog. Opt. 42 147 (2001)
  27. Chirkin A S, Rodionov A V J. Russ. Laser Res. 26 83 (2005)
  28. Belinskii A V Kvantovye Izmereniya (M.: BINOM. Lab. znanii, 2012)
  29. Kadomtsev B B Dinamika i Informatsiya 2-e izd. (M.: Redaktsiya zhurnala "Uspekhi fizicheskikh nauk", 1999)
  30. Megidish E et al. arXiv:1209.4191
  31. Chirkin A S, Belyaeva O V, Belinskii A V Zh. Eksp. Teor. Fiz. 143 48 (2013); Chirkin A S, Belyaeva O V, Belinsky A V JETP 116 39 (2013)
  32. Stoyanov I Kontrprimery v Teorii Veroyatnosti (M: Faktorial, 1999); Stoyanov J M Counterexamples In Probability (Chichester: Wiley, 1997)
  33. Zhukova I S, Malinovskaya G A, Saichev A I Analiz Sluchainykh Protsessov i Polei (Nizhnii Novgorod: Nizhegor. gos. un-t, 2006)
  34. Furusawa A, Takei N Phys. Rep. 443 97 (2007)
  35. Bargatin I V, Grishanin B A, Zadkov V N Usp. Fiz. Nauk 171 625 (2001); Bargatin I V, Grishanin B A, Zadkov V N Phys. Usp. 44 597 (2001)
  36. Elyutin P V, Klyshko D N Phys. Lett. A 149 241 (1990)
  37. Bencheikh K et al. C.R. Physique 8 206 (2007)
  38. Mandel L, Wolf E Optical Coherence And Quantum Optics (Cambridge: Cambridge Univ. Press, 1995); Mandel’ L, Vol’f E Opticheskaya Kogerentnost’ i Kvantovaya Optika (M.: Fizmatlit, 2000)
  39. Belyaeva O V, Chirkin A S Phys. Scripta 87 038101 (2013)
  40. Chirkin A S, Shutov I V Pis’ma ZhETF 86 803 (2007); Chirkin A S, Shutov I V JETP Lett. 86 693 (2007)
  41. Chirkin A S, Shutov I V Zh. Eksp. Teor. Fiz. 136 639 (2009); Chirkin A S, Shutov I V JETP 109 547 (2009)
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