Two concepts of noncontextuality in quantum mechanics

TL;DR

This paper clarifies and analyzes two distinct concepts of noncontextuality in quantum mechanics, distinguishing between ontic state-based and measurement-based definitions, and reviews their implications in the literature.

Contribution

It introduces a clear distinction between two types of noncontextuality and critically analyzes existing accounts within this framework.

Findings

Identifies two independent concepts of noncontextuality in quantum mechanics.

Provides a critical overview of literature on contextuality.

Clarifies the relationship between measurement and ontic state noncontextuality.

Abstract

There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the probability of the outcomes of every measurement independently of what other measurements are simultaneously performed. Second, an ontological model is noncontextual if any two measurements which are represented by the same self-adjoint operator or, equivalently, which have the same probability distribution of outcomes in every quantum state also have the same probability distribution of outcomes in every ontic state. I will call the first concept simultaneous noncontextuality, the second measurement noncontextuality. In the paper I will overview and critically analyze some of the most significant accounts of contextuality in the literature and subsume them under these two categories.