P -representable subset of all bipartite Gaussian separable states
M. C. de Oliveira · Physical Review A · 2004
$P$-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are $\mathrm{Sp}(2,R)\ensuremath{\bigotimes}\mathrm{Sp}(2,R)$ locally invariant. Although this special class of states can be reached by a convenient $\mathrm{Sp}(2,R)\ensuremath{\bigotimes}\mathrm{Sp}(2,R)$ transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.