Suppose I have a gaussian wigner function $W(X1, X2,p1, p1)$. For example it could be the wigner function of two modes squeezed vaccume state. I need to find the expectation value of operator $X_1P_2+P_2X_1$ and $X_2X_1+X_1X_2$ using wigner function. Basically my goal is to find covarience matrix of the two modes entangled state. How does this kind of calculaions work? as my operators are symmetric I'm trying to use the properties for seymetric operators. Thanks in advance
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