Studying quantum states: Bell nonlocality and quantum de Finetti theorems
Speaker: Paula Belzig, University of Cologne
Title: Studying quantum states: Bell nonlocality and quantum de Finetti theorems
Abstract: One of the most puzzling features of quantum mechanics is that two parties can obtain measurement statistics that cannot be reproduced by any local and classical model. These nonlocal correlations, called entanglement, between two distant parties can be exploited for information processing tasks - for example in quantum key distribution protocols, where two distant communicating parties aim to protect their secrets from a third party. Here, I will introduce two related aspects of quantum information theory and present some of my results.
On the one hand, I studied entanglement certification (e.g. via Bell nonlocality), employing numerical methods for convex optimization to better understand the usefulness and limits of quantum theory. On the other hand, I will talk about quantum de Finetti theorems, a widely used tool in the study of quantum states: if a quantum state is invariant under permutations of its subsystems, its reduction can be approximated by a mixture of tensor powers of a state on a single subsystem. Looking at a larger symmetry group than permutations has been found to lead to an exponential improvement in the approximation, and subsequently could be useful for various applications of the theorems, one of which is related to the security of quantum key distribution.