All-Possible-Couplings Approach to Measuring Probabilistic Context

TL;DR

This paper introduces a comprehensive framework for quantifying and classifying all possible types of contextual influences in systems with multiple inputs and outputs, spanning classical, quantum, and hypothetical models.

Contribution

It develops a mathematical approach using probabilistic couplings to analyze and categorize all logically possible contextual influences in complex systems.

Findings

Unified framework for classical and quantum contextuality

Quantitative measures for different types of contextual influences

Classification scheme for all logically possible contextual systems

Abstract

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly" influence them, but (iii) other inputs provide a "context" for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not empirically realizable: those that form special cases of the classical type, those that fall between the classical and quantum ones, and those that violate the quantum type. We show how one can quantify and classify all logically possible contextual influences by studying various sets of probabilistic couplings, i.e., sets of joint distributions imposed on random outputs recorded at different (mutually incompatible) values of inputs.