Werner and Wolf have proven in Phys. Rev. Lett. 86(16) (2001) a very elegant
necessary and sufficient condition for a bosonic continuous variable bipartite
Gaussian mixed quantum state to be separable. This condition is, however,
difficult to implement in practice. In the present Letter, we propose a simpler
condition which only involves the calculation of the symplectic matrix in the
Williamson diagonalization of the covariance matrix of the state under
consideration. The main tool in our construction is the observation, proved in
previous work, that the Wigner transform is covariant only under symplectic or
antisymplectic linear transformations. We also give a geometric interpretation
of our condition in terms of the orthogonal projections of “quantum blobs”..
