Equivalence between contextuality and negativity of the Wigner function for qudits
Nicolas Delfosse, Cihan Okay, Juan Bermejo-Vega, Dan E. Browne, Robert Raussendorf · New Journal of Physics · 2017
Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for quantum systems, negativity of the Wigner function and contextuality for Pauli measurements. We prove that these two notions are equivalent for multi-qudit systems with odd local dimension. For a single qudit, the equivalence breaks down. We show that there exist single qudit states that admit a non-contextual hidden variable model description and whose Wigner functions are negative.