Contextuality and Informational Redundancy

TL;DR

This paper explores how adding new variables can induce contextuality in systems of random variables, revealing that even consistent systems can exhibit this property under certain conditions, with implications for understanding informational redundancy.

Contribution

It demonstrates that adding variables can turn noncontextual systems into contextual ones, even for consistently connected systems, expanding the understanding of contextuality.

Findings

Adding variables can induce contextuality in noncontextual systems.

Consistently connected systems can exhibit contextuality when new variables incorporate unmeasured properties.

Inconsistent systems can be represented as consistent systems with similar contextuality characteristics.

Abstract

A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of contextuality, and its demonstration is trivial for inconsistently connected systems (i.e. systems with disturbance). However, it also holds for consistently connected (and even strongly consistently connected) systems, provided one acknowledges that if a given property was not measured in a given context, this information can be used in defining functions among the random variables. Moreover, every inconsistently connected system can be presented as a (strongly) consistently connected system with essentially the same contextuality characteristics.