Bounds on Epistemic Interpretations of the Quantum State from Contextuality

Claudio Garola

Terry Rudolph

Matthew Leifer, O. J. E. Maroney

We examine the relationship between quantum contextuality (in both the standard Kochen-Specker sense and in the generalized sense proposed by Spekkens) and models of quantum theory in which the quantum state is maximally epistemic. We find that preparation noncontextual models must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual. This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models. The implication from preparation noncontextual to maximally epistemic then also yields a proof of Bell's theorem from an Einstein-Podolsky-Rosen-like argument.

Vladimir I. Man’ko, Alexey A. Strakhov

Christian DE RONDE

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility (or complementarity) of certain measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal understanding of contextuality as exposed by the Kochen-Specker (KS) theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual (definite valued) properties. We will show how these two notions have been scrambled together creating an "omelette of contextuality" which has been fully widespread through a popularized "epistemic explanation" of the KS theorem according to which: The measurement outcome of the observable A when measured together with B or together with C will necessarily differ in case [A, B] = [A, C] = 0, and [B, C] /= 0. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes.

O. J. E. Maroney

A novel no-go theorem is presented which sets a bound upon the extent to which 'Ψ-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance of an underlying state of reality. The theorem applies to any Hilbert space of dimension greater than two. In the limit of large Hilbert spaces, no more than half of the overlap between quantum states can be accounted for. Unlike other recent no-go theorems no additional assumptions, such as forms of locality, invasiveness, or non-contextuality, are required.