Abstract
After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
John S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1, 195-200 (1964). Reprinted in Ref. 25, pp. 403-408.
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880-884 (1969).
J. F. Clauser and A. Shimony, “Bell's theorem: experimental tests and implications,” Rep. Prog. Phys. 41, 1881-1926 (1978).
B. S. Cirel'son, “Quantum generalization of Bell's inequality,” Lett. Math. Phys. 4, 93-100 (1980).
B. S. Cirel'son (Tsirelson), “Some results and problems on quantum Bell-type inequalities,” Hadronic J. Suppl. 8, 329-345 (1993).
Abner Shimony, “Controllable and uncontrollable nonlocality,” in S. Kamefuchi et al., ed., Proceedings of the International Symposium on the Foundations of Quantum Mechanics (Physical Society of Japan, Tokyo, 1984), pp. 225-230. See also J. Jarrett, “Bell's Theorem, Quantum Mechanics and Local Realism,” Ph.D. thesis, University of Chicago, 1983; Noûs 18, 569 (1984).
Abner Shimony, Events and processes in the quantum world, in R. Penrose and C. I. Isham, eds., Quantum Concepts in Space and Time (Clarendon Press, Oxford, 1986), pp. 182-203.
S. Popescu and D. Rohrlich, “Quantum nonlocality as an axiom,” Found. Phys. 243, 379-358 (1994).
D. Rohrlich and S. Popescu, in A. Mann and M. Revzen, eds., The Dilemma of Einstein, Podolsky, and Rosen 60 Years Later (Adam Hilger, Bristol, in press); Ann. Israel Phys. Soc. 12.
J. Grunhaus, S. Popescu, and D. Rohrlich, “Jamming nonlocal quantum correlations,” Phys. Rev. A 53, 3781 (1996).
S. Popescu and D. Rohrlich, in R. S. Cohen, M. A. Horne, and J. Stachel, eds., Quantum Potentiality, Entanglement, and Passion-at-a-Distance: Essays for Abner Shimony (Kluwer Academic, Dordrecht, in press).
Günther Krenn, “The probabilistic origin of Bell's inequality,” in D. Han, Y. S. Kim, N. H. Rubin, Y. Shih, and W. W. Zachary, eds., Proceedings of the Third International Workshop on Squeezed States and Uncertainty Relations (Maryland, August 10-13, 1993) (NASA Conference publication Nr. 3270, Greenbelt, Maryland 20771, August 1993), pp. 603-608.
Asher Peres, “Unperformed experiments have no results,” Am. J. Phys. 46, 745-747 (1978).
Asher Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).
N. Gisin and A. Peres, Maximal violation of Bell's inequality for arbitrarily large spin, Phys. Lett. A 162, 15-17 (1992).
D. Aerts, “Example of a macroscopic classical situation that violates Bell inequalities,” Lett. Nuovo Cimento 344, 107-111 (1982). The suggested analogy to two entangled spin-12 particles is challenged by the fact that the proposed expectation functions are not invariant with respect to temporal order.
Daniel M. Greenberger, Mike A. Horne, and Anton Zeilinger, “Going beyond bell's theorem,” in M. Kafatos, ed., Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Kluwer Academic, Dordrecht, 1989), pp. 73-76. See also Refs. 22 and 26.
S. M. Roy and V. Singh, “Hidden variable theories without nonlocal signalling and their experimental tests,” Phys. Lett. A 1399, 437-441 (1989).
L. Khalfin and B. Tsirelson, In P. Lahti, ed., Symposium on the Foundations of Modern Physics '85 (World Scientific, Singapore, 1985), p. 441.
P. Rastall, Found. Phys. 15, 963 (1995).
S. Summers and R. Werner, J. Math. Phys. 28, 2440, 1987.
Daniel M. Greenberger, Mike A. Horne, A. Shimony, and Anton Zeilinger, “Bell's theorem without inequalities,” Am. J. Phys. 58, 1131-1143 (1990).
N. D. Mermin, Am. J. Phys. 58, 731 (1990).
G. Krenn and A. Zeilinger, “Entangled entanglement,” Phys. Rev. A 543, 1793-1797 (1996).
John Archibald Wheeler and Wojciech Hubert Zurek, Quantum Theory and Measurement (Princeton University Press, Princeton, 1983).
N. D. Mermin, “What's wrong with these elements of reality?” Phys. Today 436, 9-10 (June 1990).
Rights and permissions
About this article
Cite this article
Krenn, G., Svozil, K. Stronger-Than-Quantum Correlations. Foundations of Physics 28, 971–984 (1998). https://doi.org/10.1023/A:1018821314465
Issue Date:
DOI: https://doi.org/10.1023/A:1018821314465