From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism

TL;DR

This paper introduces a new method for deriving noncontextuality inequalities that do not rely on determinism assumptions, enabling more robust tests of noncontextual hidden variable models in quantum mechanics.

Contribution

It generalizes noncontextuality to include both measurements and preparations, and derives inequalities that can test noncontextuality without assuming determinism.

Findings

Derived inequalities that test noncontextuality without determinism assumptions

Violations imply noncontextuality is incompatible with experimental data

Applicable to any operational theory, including future theories beyond quantum mechanics

Abstract

The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually. A noncontextual value-assignment to a projector is one that does not depend on which other projectors - the context - are measured together with it. Using a generalization of the notion of noncontextuality that applies to both measurements and preparations, we propose a scheme for deriving inequalities that test whether a given set of experimental statistics is consistent with a noncontextual model. Unlike previous inequalities inspired by the Kochen-Specker theorem, we do not assume that the value-assignments are deterministic and therefore in the face of a violation of our inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. Our approach is operational in the sense that it does not presume quantum theory: a violation of our inequality implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.