Negativity and contextuality are equivalent notions of nonclassicality

TL;DR

This paper shows that negativity and contextuality, two key concepts of quantum nonclassicality, are fundamentally equivalent when properly generalized, challenging their traditional separate roles in quantum theory.

Contribution

It introduces a refined framework that unifies negativity and contextuality, demonstrating their equivalence and providing a symmetric proof of their impossibility in quantum theory.

Findings

Negativity and contextuality are equivalent notions of nonclassicality.

A new symmetric proof shows the impossibility of noncontextuality or nonnegativity in quantum theory.

Refined definitions unify two major concepts of quantum nonclassicality.

Abstract

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 (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.