Get the density matrix from the Wigner function

[Ayushman Srivastava]

I have a 4-mode continuous variable system, and I know the 8x8 covariance matrix. I need to calculate the expectation values for some operators, which I know in terms of the creation and annihilation operators of modes. Can I calculate them directly using the covariance matrix/Wigner function? Or can I get the density matrix first and then calculate? How do I do it?