Analytic solution of the separability criterion for continuous-variable systems

By using the algebraic separability criterion of Simon, we present an explicit determination of squeezing parameters for which the P -representation condition saturates the Sp(2,R)⊗Sp(2,R) invariant separability condition for continuous variable two-party Gaussian systems. We thus give the explicit analytic formulas of squeezing parameters which establish the equivalence of the separability condition with the P -representation condition. The implications of our algebraic analysis on some of the past related works are discussed.