Ontological models and the interpretation of contextuality

TL;DR

This paper extends ontological models to better understand contextuality in quantum mechanics, revealing how measurement and preparation devices influence realism and identifying a property called deficiency that challenges symmetric interpretations.

Contribution

It introduces a generalized ontological model formalism incorporating measurement and preparation devices, and analyzes the property of deficiency related to contextuality.

Findings

Contextuality can be viewed as an interaction between system and measurement configurations.

Deficiency property breaks symmetry between preparations and measurements.

The formalism allows quantitative analysis of contextuality in realistic theories.

Abstract

Studying the extent to which realism is compatible with quantum mechanics teaches us something about the quantum mechanical universe, regardless of the validity of such realistic assumptions. It has also recently been appreciated that these kinds of studies are fruitful for questions relating to quantum information and computation. Motivated by this, we extend the ontological model formalism for realistic theories to describe a set of theories emphasizing the role of measurement and preparation devices by introducing `hidden variables' to describe them. We illustrate both the ontological model formalism and our generalization of it through a series of example models taken from the literature. Our extension of the formalism allows us to quantitatively analyze the meaning contextuality (a constraint on successful realistic theories), finding that - taken at face-value - it can be realized as a natural interaction between the configurations of a system and measurement device. However, we also describe a property that we call deficiency, which follows from contextuality, but does not admit such a natural interpretation. Loosely speaking, deficiency breaks a symmetry between preparations and measurements in quantum mechanics. It is the property that the set of ontic states which a system prepared in quantum state psi may actually be in, is strictly smaller than the set of ontic states which would reveal the measurement outcome psi with certainty.