Negativity and contextuality are equivalent notions of nonclassicality.

@article{Spekkens2008NegativityAC,
  title={Negativity and contextuality are equivalent notions of nonclassicality.},
  author={Robert W. Spekkens},
  journal={Physical review letters},
  year={2008},
  volume={101 2},
  pages={020401}
}
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory. Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that… CONTINUE READING
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