Correlations and Hyper-Correlations

Gennaro  Auletta

doi:10.4236/jmp.2011.29114

Gennaro Auletta

Abstract: Recent developments in quantum information allow for a new understanding of quantum correlations. The aim of this paper is to physically explain why quantum mechanics obeys a stronger bond than the non-sig- naling requirement or alternatively why it obeys a principle of information causality. It is shown that a physical theory violating the quantum bond allows for correlations between settings while quantum mechanics only allows for correlations between possible outcomes. In fact, correlations between settings would violate the protocols used in quantum cryptography. The conclusion is that information codification is a local operation and quantum mechanics sets the general conditions for information exchanging in our universe since it satisfies and saturates the bond that is imposed by the principle of information causality, and in so doing it also sets specific constraints on both the possible interdependencies and the possible interactions (also causal interconnections) in our universe.

Keywords: Entanglement, Non-Locality, Tsirelson Inequality, Principle of Information Causality

Cite this paper: nullG. Auletta, "Correlations and Hyper-Correlations," Journal of Modern Physics, Vol. 2 No. 9, 2011, pp. 958-961. doi: 10.4236/jmp.2011.29114.

References

[1] E. Schr?dinger, “Die Gegenw?rtige Situation in der Quantenmechanick. I-III,” Naturwissenschaften, Vol. 23, 1935, pp. 807-812, 823-828, 844-849.

[2] A. Einstein, B. Podolsky and N. Rosen, “Can Quantum- Mechanical Description of Physical Reality Be Considered Complete?” Physical Review, Vol. 47, No. 10, 1935, pp. 777-780. doi:10.1103/PhysRev.47.777

[3] G. Auletta, M. Fortunato and G. Parisi, “Quantum Me-chanics,” Cambridge University Press, Cambridge, 2009.

[4] J. S. Bell, “On Einstein Podolsky Rosen Paradox,” Phys-ics, Vol. 1, No. 3, 1964, pp. 195-200.

[5] J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters, Vol. 23, No. 15, 1969, pp. 880-884. doi:10.1103/PhysRevLett.23.880

[6] B. S. Tsirelson, “Quantum Generalizations of Bell’s In-equality,” Letters in Mathematical Physics, Vol. 4, No. 2, 1980, pp. 93-100.

[7] S. L. Braunstein, A. Mann and M. Revzen, “Maximal Violation of Bell Inequalities for Mixed States,” Physical Review Letters, Vol. 68, No. 22, 1992, pp. 3259-3261. doi:10.1103/PhysRevLett.68.3259

[8] S. Popescu and D. Rohrlich, “Quantum Nonlocality as an Axiom,” Foundations of Physics, Vol. 24, No. 3, 1994, pp. 379-85. doi:10.1007/BF02058098

[9] M. P. owski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter and M. Z. Zukowski, “Information Causality as a Physical Principle,” Nature, Vol. 461, No. 7267, 2009, pp. 1101-1104.

[10] L. Masanes, A. Acin and N. Gisin, “General Properties of Nonsignaling Theories,” Physical Review, Vol. A73, 2006, pp. 1-9.

[11] C. H. Bennett and G. Brassard, “Quantum Cryptography: Public Key Distribution and Coin Tossing,” Proceedings IEEE International Conference of Computer Systems and Signal Processing, (IEEE), Bangalore, 10-12 December 1984, pp. 175-179.

[12] A. K. Ekert, “Quantum Cryptography Based on Bell’s Theorem,” Physical Review Letters, Vol. 67, No. 6, 1991, pp. 661-663. doi:10.1103/PhysRevLett.67.661

[13] P. H. Eberhard, “Bell’s Theorem and the Different Con-cepts of Locality,” Nuovo Cimento, Vol. 46B, No. 2, 1978, pp. 392-419. doi:10.1007/BF02728628