Quantum Networks

Abstract

Entangled quantum states are remarkably rich resources for communication and computation. Today, we are witnessing the emergence of useful quantum technologies and global efforts to build the first entangled quantum communication infrastructures - the world's first quantum networks. In this thesis, we explore the potential of communication in such networks of entangled states by going beyond the typical bipartite point-to-point settings. Entanglement between more than two particles is called multipartite entanglement. Multipartite entangled states exhibit rich structures making them ideal for complex communication tasks. In the first part of this thesis, we begin with an introduction in which we establish notation, present preliminary mathematics, and explain initial bipartite quantum communication protocols. We show how to use quantum teleportation to transfer the quantum state of one particle to another, how to use quantum repeaters to extend the range of entanglement, and how to use quantum key distribution to exploit entanglement for cryptography. In the second part of this thesis, we then address quantum networks and multipartite quantum communication protocols. Here we use the mathematical abstraction of quantum graph states to theoretically explore the possibilities of real world quantum networks. We discuss the use of graph states for routing quantum information. Graph states are multipartite entangled states of quantum particles that we can manipulate with local operations on the individual particles. With these operations, which correspond to the so-called local complementation of a mathematical graph, the graph state entanglement can be redirected such that particles that never physically interacted with each other become entangled. These graph state manipulations offer fascinating possibilities. We present these possibilities of entanglement manipulation, but also some limitations of its use. For example, we prove that typical bottleneck communication problems cannot be solved in a large class of nearest-neighbor network topologies. In the light of these limitations, we further investigate the manipulation of graph state entanglement at a foundational level: We derive new and easy-to-compute invariants of graph states and study the class of circle graph states. In the third and final part of this thesis, we then explore multipartite quantum cryptography protocols with the added feature of anonymity. Exploiting the intricate features of graph state entanglement, we introduce the first protocol for anonymous quantum conference key agreement. Hopefully, quantum networks protocols like this will pave the way for a future quantum internet.