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Normally Ordered Bivariate-Normal-Distribution Forms of Two-Mode Mixed States with Entanglement Involved

Based on the technique of integration within an ordered product of operators we have demonstrated that single-mode mixed states' density matrices can be recast into the normally ordered Gaussian forms [Chin. Phys. Lett. 24 (2007) 3322]. Here we employ the Weyl ordering invariance under similar transformations to show that some two-mode mixed states with entanglement involved can be put into normally ordered form in the bivariate normal distribution too and its marginal distributions can be analysed. In this way, density operators of quantum statistics can be analogous to mathematical statistics, and calculation of variances can be simplified.