General proof of the Greenberger-Horne-Zeilinger theorem
- Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, 30 West District, Xiao-Hong Mountain, Wuhan 430071 (China)
It is proved that all states of three spin-(1/2) particles exhibiting an 'all versus nothing' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.
- OSTI ID:
- 20646001
- Journal Information:
- Physical Review. A, Vol. 70, Issue 3; Other Information: DOI: 10.1103/PhysRevA.70.032109; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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