  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 the 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
criteria, but all these criteria 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.
