  Contextuality and negativity of the Wigner function are two notions of
non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson
proved recently that these two notions coincide for qudits in odd prime
dimension. This equivalence is particularly important since it promotes
contextuality as a ressource that magic states must possess in order to allow
for a quantum speed-up. We propose a simple proof of the equivalence between
contextuality and negativity of the Wigner function based on character theory.
This simplified approach allows us to generalize this equivalence to multiple
qudits and to any qudit system of odd local dimension.
