On the P-representable subset of all bipartite Gaussian separable states

Details On the P-representable subset of all bipartite Gaussian separable states On the P-representable subset of all bipartite Gaussian separable states

2004-01-10

arxiv.org/abs/quant-ph/0401056v3

Phys. Rev. A 70, 034303 (2004).

Physics

Quantum Physics

Final version with new results added. Slightly more detailed than the accepted manuscript (to appear in Phys. Rev. A)

Scientific paper

10.1103/PhysRevA.70.034303

P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this special class of states can be reached by a convenient $Sp(2,R)\otimes Sp(2,R)$ transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.

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