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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.

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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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