Quantum communication. Non-classical correlations and their applications

TL;DR

This thesis explores advanced Bell inequalities, their optimality, and implications for quantum communication, demonstrating how non-classical correlations challenge local realism and enhance quantum cryptography and communication complexity.

Contribution

It introduces new, more general Bell inequalities involving multiple settings, proves their optimality, and extends the understanding of nonlocal models impacting quantum communication.

Findings

New Bell inequalities involving multiple settings per observer.

Extension of nonlocal model incompatibility beyond Bell's theorem.

Implications for quantum cryptography and communication complexity.

Abstract

In the first part of this thesis Bell's theorem is revisited. It points at a difference between the quantum and the classical world. This difference is often behind the advantages of solutions using quantum mechanics. New and more general versions of Bell inequalities are presented. These inequalities involve multiple settings per observer. Compared with the two-setting inequalities, the new ones reveal the non-classical character of a broader class of states. Some of them are also proven to be optimal (tight). Next, we go beyond Bell's theorem. It is shown, both in theory and in experiment, that incompatibility between quantum mechanics and realistic theories can be extended into an important class of nonlocal models. We also show that the violation of Bell inequalities disqualifies local realistic models with a limited lack of the experimenter's freedom. This, at first glance quite philosophical result, has its down-to-earth implications for quantum communication. In the second part of the thesis well-known examples of quantum communication are reviewed. Next, new results concerning quantum cryptography and quantum communication complexity are given.