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Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations

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Jacobsen, SL and Jarvis, PD (2008) Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations. Journal of Physics A: Mathematical and Theoretical, 41 (36). p. 365301. ISSN 1751-8113

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Abstract

We consider tripartite entangled states for continuous variable systems of EPR type, which generalize the famous bipartite CV EPR states (eigenvectors of conjugate choices Xl - X2, PI + P2, of the systems' relative position and total momentum variables). We give the regularized forms of such tripartite EPR states in second-quantized formulation, and derive their Wigner functions. This is directly compared with the established NaPA-like states from quantum optics. Whereas the multipartite entangled states of NaPA type have singular Wigner functions in the limit of large squeezing, r --* 00, or tanh r --* 1-'( approaching the EPR states in the bipartite case), our regularized tripartite EPR states show singular behaviour not only in the approach to the EPRtype region (s --* I in our notation), but also for an additional, auxiliary regime of the regulator (s --* .../2). While the s --* I limit pertains to tripartite CV states with singular eigenstates of the relative coordinates and remaining squeezed in the total momentum, the s --* .../2 limit yields singular eigenstates of the total momentum, but squeezed in the relative coordinates. Regarded as expectation values of displaced parity measurements, the tripartite Wigner functions provide the ingredients for generalized CHSH inequalities. Violations of the tripartite CHSH bound (B3 ~ 2) are established, with B3 ~ 2.09 in the canonical regime (s --* 1+), as well as B3~ 2.32 in the auxiliary regime (s --* .../F). PACS numbers: 03.67.-a, 42.50.-p, 03.56.Ud

Item Type: Article
Keywords: Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Page Range: p. 365301
ISSN: 1751-8113
Identification Number - DOI: 10.1088/1751-8113/41/36/365301
Additional Information: The definitive publisher authenticated version is available online at http://www.iop.org/EJ/journal/JPhysA
Date Deposited: 04 Feb 2009 00:40
Last Modified: 18 Nov 2014 03:55
URI: http://eprints.utas.edu.au/id/eprint/8286
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