Issues

 / 

1997

 / 

March

  

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
URL: https://ufn.ru/en/articles/1997/3/f/
Citation: Belinskii A V "Bell's theorem for trichotomic observables" Phys. Usp. 40 305–316 (1997)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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. Tatarskiî V I Usp. Fiz. Nauk 139 587 (1983) [Sov. Phys. Usp. 26 311 (1983)]
  2. Klyshko D N Usp. Fiz. Nauk 166 613 (1996) [Phys. Usp. 39 573 (1996)]
  3. Agarwal G S, Home D, Schleich W Phys. Lett. A 170 359 (1992)
  4. Smithey D T et al. Phys. Rev. Lett. 70 1244 (1993)
  5. Einstein A, Podolsky B, Rosen N Phys. Rev. 47 777 (1935) [Translated into Russian Usp. Fiz. Nauk 16 440 (1936)]
  6. Bohm D Quantum Theory (New York: Printice-Hall, 1951) [Translated into Russian (Moscow: Fizmatgiz, 1961)]
  7. Bell J S Physics 1 195 (1964)
  8. Belinskiî A V Pis’ma Zh. Eksp. Teor. Fiz. 59 137 (1994) [JETP Lett. 59 147 (1994)]
  9. Belinskiî A V Usp. Fiz. Nauk 164 435 (1994) [Phys. Usp. 37 413 (1994)]
  10. Klyshko D N Phys. Lett. A 218 119 (1996)
  11. Evdokimov N V et al. Usp. Fiz. Nauk 166 91 (1996) [Phys. Usp. 39 83 (1996)]
  12. Aspect A, Grangier P, Roger G Phys. Rev. Lett. 47 460 (1981); 49 91 (1982); Aspect A, Dalibar J, Roger G Phys. Rev. Lett. 49 1804 (1982)
  13. Clauser J F, Horne M A Phys. Rev. D 10 526 (1974)
  14. Shih Y H, Sergienko A V, Rubin M H, Kiess T E, Alley C O Phys. Rev. A 50 23 (1994)
  15. Clauser J F et al. Phys. Rev. Lett. 23 880 (1969)
  16. Klyshko D N Phys. Lett. A 172 399 (1993)
  17. Belinsky A V, Klyshko D N Phys. Lett. A 176 415 (1993)
  18. Belinskiî A V, Klyshko D N Usp. Fiz. Nauk 163 (8) 1 (1993) [Phys. Usp. 36 653 (1993)]
  19. Klyshko D N Fotony i Nelineînaya Optika (Photons and Nonlinear Optics, Moscow: Nauka, 1980) [Translated into English (New York: Gordon & Breach, 1988)]
  20. Mermin N D New Techniques and Idears in Quantum Meargement Theory (Ed. D M Greenberger, New York: Academy of Science, 1986) p. 422
  21. Santos E Phys. Rev. Lett. 66 1388 3227 (1991); Phys. Rev. A 46 3646 (1992); Phys. Lett. A 212 10 (1996)
  22. Eberhard P H Phys. Rev. A 47 747 (1993)
  23. Belinskiî A V Pis’ma Zh. Eksp. Teor. Fiz. 64 294 (1996) [JETP Lett. 64 325 (1996)]
  24. Santos E Found. Phys. 21 221 (1991)
  25. Garg A, Mermin N D Phys. Rev. D 35 3831 (1987)
  26. Pavi M J. Opt. Soc. Am. B 12 821 (1995)
  27. Pavi M Phys. Lett. A 209 255 (1995)
  28. Clauser J F, Horne M A Phys. Rev. D 10 526 (1974)
  29. Kwiat P G et al. Phys. Rev. A 49 3209 (1994)
  30. Elyutin P V, Klyshko D N Phys. Lett. A 149 241 (1990)
  31. Shih Y H, Rubin M H Phys. Lett. A 182 16 (1993)
  32. Greenberger D M, Horne M A, Zeilinger A Bell’s Theorem, Quantum Theory and Conceptions of the Universe (Ed. M Kafatos, Dordrecht, Holland: Kluwer, 1989) p. 69
  33. Greenberger D M et al. Am. J. Phys. 58 1131 (1990)
  34. Klyshko D N Usp. Fiz. Nauk 164 1187 (1994) [Phys. Usp. 37 1097 (1994)]
  35. Belinskiî A V Usp. Fiz. Nauk 164 231 (1994) [Phys. Usp. 37 219 (1994)]
  36. Fine A Phys. Rev. Lett. 48 291 (1982)
  37. de Muynck W M Phys. Lett. A 114 65 (1986)
  38. Boyer T H Found. Phys. 19 349 (1989)
  39. Puthoff H E Phys Rev. A 35 3266 (1987)
  40. Puthoff H E Phys. Rev. A 40 4857 (1989)

© 1918–2021 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions