QUANTUM CORRELATIONS FROM BLACK BOXES

Abstract

Quantum theory predicts the existence of correlations that violate local realism. In this thesis, we look at this fact from the reverse angle ("device-independent approach"): given that such non-local correlations are observed, what can we know about the quantum resources being used? It had been known for several years that some correlations are fingerprints of specific quantum states: this kind of blind tomography has been called "self-testing". Here we prove that every pure bipartite entangled state possesses such fingerprints, highlighting that self-testing is a generic phenomenon. Self-testing is also used in the demonstration that a proposed connection between non-locality and uncertainty relations is an artefact of cherry-picking the expression of Bell inequality equivalent under no-signalling. Finally, we report the first comprehensive geometric study of the set of quantum correlations, bringing to the fore an unexpected complexity of features.