Revisiting Quantum Contextuality

TL;DR

This paper revisits quantum contextuality, introducing concepts like extracontextuality and extravalence to connect foundational theorems and emphasize Gleason's positive role in justifying Born's rule.

Contribution

It introduces the ideas of extracontextuality and extravalence, linking Kochen-Specker and Gleason's theorems, and shifts focus to Gleason's positive implications.

Findings

Relates Kochen-Specker and Gleason's theorems through extracontextuality and extravalence.

Highlights Gleason's theorem as a positive result justifying Born's rule.

Provides a new perspective on quantum contextuality concepts.

Abstract

The purpose of this note is to complete the interesting review on quantum contextuality [1] that appeared recently. In particular we will introduce and discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems, and also to shift the emphasis from the first to the second one. We will also argue that whereas Kochen-Specker's is essentially a negative result (a no-go theorem), Gleason's is a positive one since it provides a mathematical justification of Born's rule. The link between these issues is provided by a specific quantum feature that we call extravalence.