Abstract
We consider the question of factorizability in tensor product spaces, and argue that the correlations associated with entangled states are even more problematic in the general case involving any tensor product of Hilbert spaces, than in the Einstein, Podolsky, and Rosen case with only two [1].
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References
D. Greenberger, M. A. Horne, and A. Zeilinger consider the case of three subsystems inBell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer, Dordrecht, 1989).
A. Einstein, B. Podolsky, and N. Rosen, ‘Can quantum-mechanical description of physical reality be considered complete?’Phys. Rev. 47, 777–780 (1935). See also E. Schrödinger, ‘Discussion of probability relations between separated systems,’Proc. Camb. Phil. Soc. 31, 555–562 (1935); ‘Probability relations between separated systems,’Proc. Camb. Phil. Soc. 32, 446–452 (1936). D. Bohm,Quantum Theory (Prentice-Hall, Englewood Cliffs, N.J. 1951), pp. 614–619.
J. von Neumann,Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932). See also S. Bergia, ‘Quantum mechanical correlations between subsystems as an aspect of tensor algebra,’Ann. Fond. Louis de Broglie 18, 53–79 (1993); A. Shimony. ‘Degree of entanglement,’ to appear inFundamental Problems in Quantum Theory, D. Greenberger, ed., Ann. N. Y. Acad. Sci., 1995.
S. Bergia and F. Cannata, ‘Two-particle quantum mechanical correlations and local-realistic theories for non-binary observables,’ inBell's Theorem and the Foundations of Modern Physics, A. van der Merweet al., eds. (World Scientific, Singapore, 1992).
W. H. Furry, ‘Note on the quantum-mechanical theory of measurement,’Phys. Rev. 49, 393–399 (1936); and ‘Remarks on measurement in quantum theory.’Phys. Rev. 49, 476 (1936). See also D. Bohm and Y. Aharonov, ‘Discussion of experimental proof for the paradox of Einstein, Rosen and Podolsky.’Phys. Rev. 108, 1070–1076 (1957).
V. Capasso, D. Fortunato, F. Selleri, ‘Sensitive observables of quantum mechanics’,Internat. J. Theoret. Phys. 7, 319–326 (1973).
D. Fortunato and F. Selleri, ‘Sensitive observables on infinite-dimensional Hilbert spaces,’Internat. J. Theoret. Phys. 15, 333–338 (1976).
J. S. Bell, ‘On the Einstein-Podolsky-Rosen paradox,’Physics 1, 195–200 (1964).
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Afriat, A. Probability relations involving several subsystems. Found Phys Lett 8, 467–480 (1995). https://doi.org/10.1007/BF02186582
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DOI: https://doi.org/10.1007/BF02186582