The Exclusivity Principle and the Set of Quantum Correlations

TL;DR

This paper explores how the Exclusivity principle can characterize quantum correlations and potentially explain quantum contextuality by analyzing its activation effects and limitations.

Contribution

It demonstrates the application of the Exclusivity principle to complex scenarios, showing its potential to single out quantum distributions and discussing its limitations.

Findings

The Exclusivity principle singles out maximum quantum values for some inequalities.

Activation effects can help prove the principle's effectiveness in certain cases.

The principle may not fully explain quantum contextuality, but shows promising results.

Abstract

The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the Exclusivity principle singles out the maximum quantum value for some important Bell and noncontextuality inequalities. We can get better results if we apply the E principle to more sophisticated scenarios. This happens because this principle exhibits activation effects: a distribution satisfying this principles does not necessarily satisfy it when combined with other distributions. Activation effects can be used to prove that the Exclusivity principle singles out the set of quantum distributions for the most simple noncontextuality inequality. It is still not known if the exclusivity principle solves the problem of explaining quantum contextuality completely, but many results have been proven that support the conjecture that it might. The main purpose of this thesis is to discuss in detail the situations in which the E principle can be used to rule out distributions outside the quantum set.