Resource characterisation of quantum entanglement and nonlocality in multipartite settings

TL;DR

This paper investigates the resource properties of entanglement and nonlocality in multipartite quantum systems, proposing new theories and examples that enhance understanding of quantum network usefulness and fundamental principles.

Contribution

It introduces a resource theory for multipartite entanglement, demonstrates genuine multipartite nonlocality in networks, and explores the importance of topology and superactivation phenomena.

Findings

Connected bipartite networks are genuinely multipartite nonlocal.

Topology influences entanglement in mixed states.

First example of superactivation of GMNL.

Abstract

Quantum technologies are enjoying an unprecedented popularity, and some applications are already in the market. This thesis studies two phenomena that are behind a lot of quantum technologies: entanglement and nonlocality. We focus on multipartite systems, and ask what configurations of those systems are more useful than others. 'Usefulness' takes on different meanings depending on the context, but, roughly speaking, we aim for more entanglement or more nonlocality. Chapter 2 develops a resource theory of entanglement with a unique multipartite maximally entangled state. Chapter 3 shows that any connected network of bipartite pure entangled states is genuine multipartite nonlocal (GMNL). Chapter 4 shows that, unlike in the case of pure states, topology is crucial to determine whether networks of bipartite mixed entangled states are genuine multipartite entangled. We also obtain, to our knowledge, the first example of superactivation of GMNL. In a departure from the main ideas explored in previous chapters, Chapter 5 is devoted to developing a physical principle inspired by a seminal result in epistemics. We contend that the principle must hold for any theory of Nature and intend for it to rule out post-quantum theories which are consistent with experimentally observed results.