8

2

We know that the Wigner function of a Gaussian quantum state is (up to a constant) a Gaussian distribution. The first moment and the covariance of this distribution uniquely specify a quantum state. Therefore a Wigner function uniquely determines a Gaussian state.

Are there any similar statements applying to non-Gaussian states?

2

Thanks! I also would like to share here that for any observable $H(x,p)$ of the form $H(x,p)=T(p)+U(x)$, its expectational value could be calculated by $\int W(x,p) H(x,p) dx dp$. (c.f. this stack exchange post)

– taper – 2018-08-24T13:55:38.467