Negativity and contextuality are equivalent notions of 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.

5 pages, published version (modulo some supplementary material)

References in corpus (1)

• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements

Cited by in corpus (5)

• Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
• Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
• Nonclassicality of states and measurements by breaking classical bounds on statistics
• Quantum-Bayesian Coherence
• Economical ontological models for discrete quantum systems