Entanglement versus negative domains of Wigner functions

Abstract

We show that $s$ waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of $s$ waves which allows us to perform the calculations analytically. This class includes a Gaussian, a maximally entangled as well as a ``shell'' state.