Separability criteria for continuous-variable systems
Kazuo Fujikawa · Physical Review A · 2009
A general separability condition on the second moment (covariance matrix) for continuous-variable two-party systems is derived by an analysis analogous to the derivation of Kennard's uncertainty relation without referring to the non-negativity of the partially transposed density matrix. This separability criterion is generally more stringent than that used by Simon which is based on the non-negativity of partially transposed density matrix, and thus this criterion may be useful in the analysis of general continuous two-party systems. Another separability criterion used by Duan et al. is shown to be generally weaker than that of Simon. We thus have a hierarchy of separability criterions, but all these criterions when combined with suitable squeezing become equivalent at the boundary of the $P$-representation condition and thus turned out to be sufficient to analyze the separability of two-party Gaussian systems.