Analytic solution of the separability criterion for continuous-variable systems
Kazuo Fujikawa · Physical Review A · 2009
By using the algebraic separability criterion of Simon, we present an explicit determination of squeezing parameters for which the $P$-representation condition saturates the $\text{Sp}(2,R)\ensuremath{\bigotimes}\text{Sp}(2,R)$ 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.