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

Citation

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


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Copyright Statement

The definitive publisher authenticated version is available online at http://www.iop.org/EJ/journal/JPhysA

Official URL: http://www.iop.org/EJ/journal/JPhysA

DOI: doi:10.1088/1751-8113/41/36/365301

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 X1 − X2, P1 + 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 NOPA-like states from quantum optics. Whereas the multipartite entangled states of NOPA type have singular Wigner functions in the limit of large squeezing, r , 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 EPR-type region (s 1 in our notation), but also for an additional, auxiliary regime of the regulator . While the s 1 limit pertains to tripartite CV states with singular eigenstates of the relative coordinates and remaining squeezed in the total momentum, the 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 in the canonical regime (s 1+), as well as in the auxiliary regime . PACS numbers: 03.67.−a, 42.50.−p, 03.56.Ud 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 Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Mathematical Physics
Research Field:Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Jacobsen, SH (Miss Sol Jacobsen)
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:53979
Year Published:2008
Web of Science® Times Cited:2
Deposited By:Physics
Deposited On:2009-02-04
Last Modified:2009-06-10
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