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0001804864
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Going beyond Bell's theorem
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M. Kafatos, ed. Kluwer Academic, Dordrecht, The Netherlands
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D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going beyond Bell's theorem," in Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1989), p.69; see also D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, Am. J. Phys. 58, 1131-43 (1990). The GHZ experiment was recently realized successfully in the laboratory by D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345-1349 (1999).
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Bell's Theorem, Quantum Theory and Conceptions of the Universe
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Greenberger, D.M.1
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D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going beyond Bell's theorem," in Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1989), p.69; see also D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, Am. J. Phys. 58, 1131-43 (1990). The GHZ experiment was recently realized successfully in the laboratory by D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345-1349 (1999).
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0342989546
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D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going beyond Bell's theorem," in Bell's Theorem, Quantum Theory and Conceptions of the Universe, M. Kafatos, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1989), p.69; see also D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, Am. J. Phys. 58, 1131-43 (1990). The GHZ experiment was recently realized successfully in the laboratory by D. Bouwmeester, J-W Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345-1349 (1999).
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Zeilinger, A.5
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A review of many joint proofs of the BKS and Bell theorems, together with references to the original papers, can be found in P. K. Aravind, Phys. Lett. A 262, 282 (1999).
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J. S. Bell, Rev. Mod. Phys. 38, 447-52 (1966), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). S. Kochen and E. P. Specker, J. Math. Mech. 17, 59-88 (1967). The BKS theorem is a special case of the more powerful theorem proved in A. M. Gleason, J. Math. Mech. 6, 885 (1957).
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Bell, J.S.1
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Cambridge University Press, Cambridge
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J. S. Bell, Rev. Mod. Phys. 38, 447-52 (1966), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). S. Kochen and E. P. Specker, J. Math. Mech. 17, 59-88 (1967). The BKS theorem is a special case of the more powerful theorem proved in A. M. Gleason, J. Math. Mech. 6, 885 (1957).
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Speakable and Unspeakable in Quantum Mechanics
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Bell, J.S.1
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4243882278
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J. S. Bell, Rev. Mod. Phys. 38, 447-52 (1966), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). S. Kochen and E. P. Specker, J. Math. Mech. 17, 59-88 (1967). The BKS theorem is a special case of the more powerful theorem proved in A. M. Gleason, J. Math. Mech. 6, 885 (1957).
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Kochen, S.1
Specker, E.P.2
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J. S. Bell, Rev. Mod. Phys. 38, 447-52 (1966), reprinted in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987). S. Kochen and E. P. Specker, J. Math. Mech. 17, 59-88 (1967). The BKS theorem is a special case of the more powerful theorem proved in A. M. Gleason, J. Math. Mech. 6, 885 (1957).
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Gleason, A.M.1
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J. S. Bell, Physics 1, 195-200 (1964). Reprinted in the book quoted in Ref. 6.
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A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935); see also D.Bohm, Quantum Theory (Prentice Hall, Englewood Cliffs, NJ, 1951).
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0041644773
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note
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See, however, Mermin's paper in Ref. 9 for a thought-provoking theoretical argument in support of noncontextuality.
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19
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0042145654
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note
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A more detailed explanation of this assertion is as follows: When Alice measures a particular observable on her qubits, she collapses them into the two-dimensional subspace associated with a particular eigenvalue (+1 or -1) of that observable. The correlations in state (1) then dictate that Bob's qubits collapse into the same two-dimensional subspace of their Hubert space. If Bob subsequently measures the same observable as Alice, either alone or in combination with any other observables that commute with it, his qubits remain within the selected two-dimensional subspace and he definitely obtains the same eigenvalue as Alice for the common observable measured.
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20
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6744247129
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A "non-demolition" measurement on a set of qubits can be carried out by coupling them to ancilliary qubits and carrying out the usual (destructive) measurements on the ancilliary qubits. A quantum circuit, consisting of a sequence of one-and two-qubit gates, can be designed to implement any non-demolition measurement. However the practical implementation of the basic two-qubit XOR (or "controlled-not") gate is still in its infancy, and so the ability to carry out the required non-demolition measurements is still a little open. For an alternative approach to the measurement of sequences of commuting two-qubit observables, see C Simon, M. Zukowski, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 85, 1783 (2000).
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We have replaced Mermin's observables by a slightly different set suggested in M. Kernaghan and A. Peres, Phys. Lett. A 198, 1-5 (1995).
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