Bernstein's paradox of entangled quantum states

A.V. Belinskii^a, b, A.S. Chirkin^a, b
^aLomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
^bInternational 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.

PACS: 03.65.Ud, 42.65.Lm (all)
DOI: 10.3367/UFNe.0183.201311e.1231
URL: https://ufn.ru/en/articles/2013/11/d/
Web of Science

000331111800004
Scopus

2-s2.0-84893841610
ADS NASA

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, accepted: 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) ↓

A.V. Belinsky, M.Kh. Shulman “Quantum nature of a nonlinear beam splitter” Phys. Usp. 57 1022–1034 (2014)
A.V. Belinsky “Wigner's friend paradox: does objective reality not exist?” Phys. Usp. 63 1256–1263 (2020)
A.V. Belinsky, A.A. Klevtsov “Nonlocal classical "realism" and quantum superposition as the nonexistence of definite pre-measurement values of physical quantities” Phys. Usp. 61 313–319 (2018)
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 principle” Sov. Phys. Usp. 31 74–85 (1988)
A.M. Zheltikov “The critique of quantum mind: measurement, consciousness, delayed choice, and lost coherence” Phys. Usp. 61 1016–1025 (2018)
A.V. Belinskii “Bell’s theorem for trichotomic observables” Phys. Usp. 40 305–316 (1997)
D.N. Klyshko “The Einstein-Podolsky-Rosen paradox for energy-time variables” Sov. Phys. Usp. 32 555–563 (1989)
V.P. Demutskii, R.V. Polovin “Conceptual problems in quantum mechanics” Sov. Phys. Usp. 35 (10) 857–896 (1992)
A.V. Belinskii “Bell’s theorem without the hypothesis of locality” Phys. Usp. 37 219–222 (1994)
B.B. Kadomtsev “Irreversibility in quantum mechanics” Phys. Usp. 46 1183–1201 (2003)
A.V. Belinsky “On David Bohm's 'pilot-wave' concept” Phys. Usp. 62 1268–1278 (2019)
V.L. Gorshenin, B.N. Nougmanov, F.Ya. Khalili “On 'Schrödinger's cat' fringes” Phys. Usp. 67 938–942 (2024)
V.V. Mityugov “The tree of paradox” Phys. Usp. 36 (8) 744–753 (1993)
M.B. Mensky “Measurability of quantum fields and the energy—time uncertainty relation” Phys. Usp. 54 519–528 (2011)
B.B. Kadomtsev “Classical and quantum irreversibility” Phys. Usp. 38 923–929 (1995)
A.V. Belinskii “Bell’s paradoxes without the introduction of hidden variables” Phys. Usp. 37 413–419 (1994)
A.A. Grib “On the problem of the interpretation of quantum physics” Phys. Usp. 56 1230–1244 (2013)
V.S. Pronskikh “Measurement problems: contemporary discussions and models” Phys. Usp. 63 192–200 (2020)
A.V. Belinskii “Regular and quasiregular spectra of disordered layer structures” Phys. Usp. 38 653–664 (1995)
M.V. Lebedev, O.V. Misochko “On the question of a classical analog of the Fano problem” Phys. Usp. 65 627–640 (2022)

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