Equivalence between contextuality and negativity of the Wigner function for qudits

TL;DR

This paper proves that for qudits of odd prime dimension, contextuality and Wigner function negativity are equivalent, extending the result to multiple qudits and general odd dimensions, highlighting their role as quantum resources.

Contribution

It provides a simplified proof of the equivalence between contextuality and Wigner function negativity, generalizing it to multi-qudit systems and all odd local dimensions.

Findings

Equivalence between contextuality and negativity for single qudits in odd prime dimensions

Generalization of the equivalence to multiple qudits

Extension to any qudit system with odd local dimension

Abstract

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.