What does an experimental test of quantum contextuality prove or disprove?

TL;DR

This paper critically examines the experimental testability of quantum contextuality, introducing a stronger condition called ontological faithfulness to make Bell-Kochen-Specker theorem proofs robust against finite-precision approximations.

Contribution

It introduces ontological faithfulness, a stronger non-contextuality condition, enabling robust experimental tests of quantum contextuality at finite precision.

Findings

Finite-precision approximations challenge traditional tests

Ontological faithfulness strengthens non-contextuality constraints

Experimental refutation of ontologically faithful non-contextual models possible

Abstract

The possibility to test experimentally the Bell-Kochen-Specker theorem is investigated critically, following the demonstrations by Meyer, Kent and Clifton-Kent that the predictions of quantum mechanics are indistinguishable (up to arbitrary precision) from those of a non-contextual model, and the subsequent debate to which extent these models are actually classical or non-contextual. The present analysis starts from a careful consideration these "finite-precision" approximations. A stronger condition for non-contextual models, dubbed <ontological faithfulness>, is exhibited. It is shown that it allows to formulate approximately the constraints in Bell-Kochen-Specker theorems such as to render the usual proofs robust. As a consequence, one can experimentally test to finite precision ontologically faithful non-contextuality, and thus experimentally refute explanations from this smaller class. We include a discussion of the relation of ontological faithfulness to other proposals to overcome the finite precision objection.