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Volumn 15, Issue 4, 2002, Pages 397-405

Bell's theorem without inequalities and only two distant observers

Author keywords

Bell's theorem without inequalities; Kochen Specker theorem

Indexed keywords


EID: 0036445752     PISSN: 08949875     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021272729475     Document Type: Article
Times cited : (73)

References (27)
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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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    • 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).
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1345-1349
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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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    • note
    • See, however, Mermin's paper in Ref. 9 for a thought-provoking theoretical argument in support of noncontextuality.
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    • note
    • 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.
  • 20
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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).
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 1783
    • Simon, C.1    Zukowski, M.2    Weinfurter, H.3    Zeilinger, A.4
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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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    • Kernaghan, M.1    Peres, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.