Measurement contextuality is implied by macroscopic realism

TL;DR

This paper demonstrates that measurement contextuality is a necessary consequence of macroscopic realism in ontological quantum theories, highlighting the unique role of the Beltrametti-Bugajski model and implications for the measurement problem.

Contribution

It provides a proof that the Beltrametti-Bugajski model is the only measurement non-contextual indeterminist model for projective measurements in Hilbert spaces of dimension greater than two.

Findings

Beltrametti-Bugajski model is unique in measurement non-contextuality.

Von Neumann non-contextuality implies non-contextuality for unsharp measurements.

Relaxing non-contextuality is necessary to address the measurement problem.

Abstract

Ontological theories of quantum mechanics provide a realistic description of single systems by means of well-defined quantities conditioning the measurement outcomes. In order to be complete, they should also fulfil the minimal condition of macroscopic realism. Under the assumption of outcome determinism and for Hilbert space dimension greater than two, they were all proved to be contextual for projective measurements. In the recent years a generalized concept of non-contextuality was introduced that applies also to the case of outcome indeterminism and unsharp measurements. It was pointed out that the Beltrametti-Bugajski model is an example of measurement non-contextual indeterminist theory. Here we provide a simple proof that this model is the only one with such a feature for projective measurements and Hilbert space dimension greater than two. As a corollary, von Neumann measurement non-contextuality implies non-contextuality for unsharp measurements. By noting that the Beltrametti-Bugajski model does not satisfy the condition of macroscopic realism, we arrive at the conclusion that the only way to solve the measurement problem in the framework of an ontological theory is relaxing the hypothesis of non-contextuality in its generalized sense.