Non-locality, Contextuality and Transition sets

TL;DR

This paper explores quantum non-locality and contextuality through transition sets, providing graphical insights into Bell inequality violations and introducing a new form of measurement ordering contextuality that hidden variable theories must exhibit.

Contribution

It introduces a transition set framework for analyzing non-locality and contextuality, and defines measurement ordering contextuality as a new phenomenon in quantum theory.

Findings

Graphical illustration of Bell inequality violations

Identification of measurement ordering contextuality

Hidden variable theories must exhibit measurement ordering contextuality

Abstract

We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measures of non-local transition sets. We also introduce a new form of contextuality, {\em measurement ordering contextuality}, i.e. there exists commuting operators $\hat{\mathcal{A}}$ and $\hat{\mathcal{B}}$ such that the outcome for $\hat{\mathcal{A}}$ depends on whether we measured $\hat{\mathcal{B}}$ before or after $\hat{\mathcal{A}}$. It is shown (excluding retro-causal and/or conspiratorial theories) that any hidden variable theory capable of reproducing the quantum statistics has to have this property. This generalizes yet another feature of the hidden variable theory of deBroglie and Bohm.