Methodological notes

Bell’s theorem for trichotomic observables

Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

Bell’s paradoxes, due to the fundamental properties of light and the nature of the photon, are discussed within a single framework with a view to checking the hypothesis that a stationary, non-negative, joint probability distribution function exists. This hypothesis, related to the local theory of hidden parameters as a possible interpretation of quantum theory, enables experimentally verifiable Bell’s inequalities to be formulated. The dependence of these inequalities on the number of observers V is considered. Quantum theory predicts the breakdown of Bell’s inequalities in optical experiments. It is shown that as V increases, the requirements on the quantum effectiveness of the detector, η, are reduced from η>2/3 at V=2 to η>1/2 for V \rightarrow \infty . Examples of joint probability distribution functions are given for illustrative purposes, and a way to resolve the Greenberg-Horne-Zeilinger (GHZ) paradox is suggested.

PACS: 03.65.Bz
DOI: 10.1070/PU1997v040n03ABEH000225
Citation: Belinskii A V "Bell's theorem for trichotomic observables" Phys. Usp. 40 305–316 (1997)
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Оригинал: Белинский А В «Теорема Белла для трихотомных наблюдаемых» УФН 167 323–335 (1997); DOI: 10.3367/UFNr.0167.199703h.0323

References (40) Cited by (13) Similar articles (20) ↓

  1. A.V. Belinskii “Bell’s theorem without the hypothesis of locality37 219–222 (1994)
  2. B.B. Kadomtsev “Irreversibility in quantum mechanics46 1183–1201 (2003)
  3. A.V. Belinskii “Bell’s paradoxes without the introduction of hidden variables37 413–419 (1994)
  4. A.V. Belinskii, A.S. Chirkin “Bernstein’s paradox of entangled quantum states56 1126–1131 (2013)
  5. N.V. Evdokimov, D.N. Klyshko et alBell’s inequalities and EPR-Bohm correlations: working classical radiofrequency model39 83–98 (1996)
  6. A.V. Belinsky, M.Kh. Shulman “Quantum nature of a nonlinear beam splitter57 1022–1034 (2014)
  7. 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)
  8. M.B. Mensky “Measurability of quantum fields and the energy—time uncertainty relation54 519–528 (2011)
  9. D.N. Klyshko “The Einstein-Podolsky-Rosen paradox for energy-time variables32 555–563 (1989)
  10. L.A. Rivlin “Photons in a waveguide (some thought experiments)40 291–303 (1997)
  11. A.V. Belinsky “Wigner's friend paradox: does objective reality not exist?63 (12) (2020)
  12. V.V. Mityugov “Thermodynamics of simple quantum systems43 631–637 (2000)
  13. G. Oppen “Objects and environment39 617–622 (1996)
  14. Yu.L. Klimontovich “Entropy and information of open systems42 375–384 (1999)
  15. A.V. Belinsky “On David Bohm's 'pilot-wave' concept62 1268–1278 (2019)
  16. I.E. Mazets “Kinetic equation including wave function collapses41 505–507 (1998)
  17. S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles42 573–590 (1999)
  18. Yu.I. Vorontsov “The uncertainty relation between energy and time of measurement24 150–158 (1981)
  19. A.V. Belinsky, A.A. Klevtsov “Nonlocal classical "realism" and quantum superposition as the nonexistence of definite pre-measurement values of physical quantities61 313–319 (2018)
  20. A.V. Belinskii “Regular and quasiregular spectra of disordered layer structures38 653–664 (1995)

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