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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
Authors/Creators:	Jacobsen, SL and Jarvis, PD
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
ISSN:	1751-8113
DOI / ID Number:	https://doi.org/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
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