Abstract
The investigation of the foundations of quantum mechanics has received momentous stimulation when, in 1964, John Bell established his famous theorem1. It is specifically remarkable that Bell’s work not only triggered an enormous amount of theoretical work, it also gave rise to an extensive series of experiments. Both the discussion and the experiments focussed on the quantum mechanical correlations in two-particle systems. Recently, an extension to systems with more than two particles was found with rather interesting novel properties2. In the present paper we shall firstly point out the similarities and the differences between the two situations and secondly we shall briefly discuss some new aspects concerning entangled states consisting of more than two particles partly by further generalizing the quantum states considered.
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References
J.S. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics 1, 195–200 (1964)
reprinted in J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge U.P., Cambridge, 1987).
D.M. Greenberger, M. Horne, and A. Zeilinger, “Going beyond Bell’s theorem,” in Bell’s Theorem, Quantum Theory,and Conceptions of the Universe, edited by M. Kafatos, Kluwer Academic, Dordrecht, The Netherlands (1989), pp. 73–76.
D.M. Greenberger, M.A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities”, Am. J. Phys. 58, 1131–1143 (1990).
S.M. Barnett, S.J.D. Phoenix and D.T. Pegg, “Entropy, information and quantum optical correlations”, this conference. A. Ekert, “Quantum Cryptography based on Bell’s theorem”, this conference.
A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47 777–780 (1935).
M. A. Horne and A. Zeilinger, “A Bell-type EPR experiment using linear momenta”, in Symposium on the Foundations of Modern Physics,edited by P. Lahti and P. Mittelstaedt (World Scientific, Singapore, 1985), pp. 435–439.
M.A. Horne, A. Shimony, and A. Zeilinger, “Two-particle interferometry,” Phys. Rev. Lett. 62 2209–2212 (1989).
J.G. Rarity and P.R. Tapster, “Experimental violation of Bell’s inequality based on phase and momentum”, Phys. Rev. Lett. 64 2495–2498 (1990).
N.D. Mermin, “Quantum mysteries revisited”, Am. J. Phys. 58 731–734 (1990);
N.D. Mermin and “What’s wrong with these elements of reality?” Phys Today 43 (6), 9–11 (1990);
N.D. Mermin “Extreme quantum entanglement in a superposition of macroscopically distinct states”, Phys. Rev. Lett. 65 1838–1840 (1990).
E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik”, Naturwissenschaften 23, 807–812, 823–828, 844–849 (1935).
E. Schrödinger English translation in “Quantum Theory and Measurement”, J.A. Wheeler and W.H. Zurek, Eds., Princeton Univ. Press, Princeton (1983).
M. Redhead, “Incompleteness, Nonlocality, and Realism”, Clarendon, Oxford (1987).
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Zeilinger, A., Greenberger, D.M., Horne, M.A. (1992). Bell’s Theorem without Inequalities and Beyond. In: Tombesi, P., Walls, D.F. (eds) Quantum Measurements in Optics. NATO ASI Series, vol 282. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3386-3_30
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DOI: https://doi.org/10.1007/978-1-4615-3386-3_30
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