Hudson's theorem tells us that a pure state has non-negative Wigner function iff it's Gaussian. This was originally proven in [Hudson 1974], and then generalised to multidimensional systems in [Soto and Claverie 1983]. Accessing these old papers is not however the easiest thing in the world.
Is there any more modern/easily accessible proof of this theorem? Alternatively, having the theorem's proof reproduced here would also make it much easier to access.
