Greenberger-Horne-Zeilinger nonlocality for continuous variable systems

Details Greenberger-Horne-Zeilinger nonlocality for continuous variable systems Greenberger-Horne-Zeilinger nonlocality for continuous variable systems

2001-03-14

arxiv.org/abs/quant-ph/0103082v2

Phys. Rev. A 65, 044102 (2002)

Physics

Quantum Physics

RevTEX; comments are welcomed; new version with minor changes

Scientific paper

10.1103/PhysRevA.65.044102

As a development of our previous work, this paper is concerned with the Greenberger-Horne-Zeilinger (GHZ) nonlocality for continuous variable cases. The discussion is based on the introduction of a pseudospin operator, which has the same algebra as the Pauli operator, for each of the $N$ modes of a light field. Then the Bell-CHSH (Clauser, Horne, Shimony and Holt) inequality is presented for the $N$ modes, each of which has a continuous degree of freedom. Following Mermin's argument, it is demonstrated that for $N$-mode parity-entangled GHZ states (in an infinite-dimensional Hilbert space) of the light field, the contradictions between quantum mechanics and local realism grow exponentially with $N$, similarly to the usual $N$-spin cases.

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