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”..

    Source link


    Leave A Reply