Multipartite Quantum Entanglement and Security

Multipartite Quantum Entanglement and Security-Entanglement is one of the most counterintuitive phenomena in quantum physics and has long puzzled scientists and philosophers alike. Besides raising a challenge to local realistic worldviews, entanglement plays a key role in quantum technologies today. From unconditionally secure quantum communication to cutting-edge quantum computers, entanglement provides a game-changing quantum advantage in many applications. Entanglement forms the backbone of such technologies, and many experiments demonstrating it for many parties have been performed recently. A key ingredient in such experiments is the ability to verify that entanglement does indeed exist in the state that is created. This is important not only from a fundamental point of view, but also when one relies on the entanglement for security. Certifying the presence of entanglement is extremely challenging when many particles and multiple dimensions of each particle are involved. Such complex quantum states have only recently been created in the lab, and have immense potential for enhancing quantum communication protocols. The first aim of this project is to develop practical ways to measure and confirm the presence of entanglement in multipartite high-dimensional states. In order to do so, we will develop entanglement certification schemes that can cope with only a limited amount of information available. The use of high-dimensional states in quantum networks has the potential to enable communication protocols with record information capacities and unprecedented levels of security. The second goal of this project is develop new cryptographic protocols that specifically use multipartite high-dimensional entangled states as information carriers. We will focus on developing a layered quantum key distribution scheme that allows different layers of information to be shared among many parties in an asymmetric but unconditionally secure fashion. Further, we will design communication protocols where the amount of trust varies for the different parties involved. This is an extremely relevant scenario given the importance of information security in our society today. Modern methods for creating multi-photon entangled states suffer from drastically low count rates. The final goal of this project is to identify the limitations of state-of-the-art sources of high-dimensional entanglement, and develop methods to overcome these limitations. We will investigate unique combinations of optical elements that are essential for creating and manipulating multipartite high-dimensional photonic entanglement in the lab. Techniques for creating such states are in their infancy, with only one such entangled state created so far. In addition to developing methods for verifying entanglement in such states, this project will open the door towards creating a vast array of high-dimensional entangled states in the lab, with immediate applications in the quantum communication protocols designed as part of it.

In this project we investigated the phenomenon of quantum entanglement for its potential for proving security for multi-party-communication. Entanglement is a phenomenon, which allows to prove exclusivity of a shared state through measured correlations in distant labs. This exclusivity, i.e. the certainty that no other physical system could potentially be correlated with the system under investigation, can then be used to leverage the measurements upon this system for a shared cryptographic key. In the meantime, communicating with two quantum bits, i.e. two systems that can encode 0 and 1 into some physical degree of freedom, such as the horizontal or vertical polarisation for single photons, have become a community standard. In our project we wanted to transcend this paradigm and focus on more than two particles, especially with more than two physically discernable degrees of freedom amenable to information encoding. This was outstandingly successul, leading to a multitude of publications resulting from this project. Most notably, a new protocol, which allows to harness high-dimensional multipartite entanglement for creating multiple keys for subgroups of participants in a multi-party communication scenario. In the course of this investigation multiple further applications were discovered, among them novel experimental schemes for the implementation of high-dimensional and multipartite entanglement and novel methods for certifying entanglement in such systems.