Assumption-free derivation of the Bell-type criteria of contextuality/nonlocality

TL;DR

This paper presents a method to derive Bell-type criteria for contextuality and nonlocality without relying on traditional assumptions, applicable even to systems with signaling, by using the Contextuality-by-Default framework.

Contribution

It introduces an assumption-free derivation of Bell-type criteria applicable to both signaling and non-signaling systems, expanding the theoretical understanding of contextuality.

Findings

Derived Bell-type criteria for inconsistently connected systems

Specialized criteria for consistently connected systems

Framework applicable without assumptions like locality or free choice

Abstract

Bell-type criteria of contextuality/nonlocality can be derived without any falsifiable assumptions, such as context-independent mapping (or local causality), free choice, or no-fine-tuning. This is achieved by deriving Bell-type criteria for inconsistently connected systems (i.e., those with disturbance/signaling), based on the generalized definition of contextuality in the Contextuality-by-Default approach, and then specializing these criteria to consistently connected systems.