  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.
