Entanglement-Based Certification of Quantum Technologies

Entanglement is a form of correlation between the measurement outcomes of different measurable quantities of two or more quantum systems that persists despite the fact that the laws of quantum mechanics prevent these quantities from being simultaneously measureable. That is, even though we cannot meaningfully speak of the measurement results for the individual systems as being properties of the system prior to the measurement, and even though we have the freedom to choose different non-compatible measureable quantities, the outcomes can be perfectly correlated. Aside from its conceptual significance for quantum theory and its many applications in quantum communication, for instance, for so-called quantum teleportation, entanglement is a ubiquitous feature of many, if not all, currently developed quantum technologies, in particular, in the domain of quantum computation and quantum simulation. As such, the detection and quantification of entanglement, and the characterization of the entanglement structures in complex quantum systems can serve as an indicator for the quality of control over the system in the laboratory. In this spirit, one may regard the presence of entanglement as a form of certificate for the quantum nature of a device. This project in the field of quantum information theory aims to develop such entanglement-based certification tools for quantum technologies in the areas of quantum computation, quantum simulation and quantum communication. Even just a few years in the past, quantum information research has been subject to a divide between abstract and idealized theoretical considerations on the one hand, and severe experimental limitations on the number, quality and control over quantum systems, on the other hand. As this gap is rapidly closing in the light of recent technological advances, pragmatic new tools and solutions are required in both theory and experiment. This research project is intended as a capstone that is both supported by the aforementioned advances while itself contributing to bridging the gap. The project will provide new theoretical methods for the detection and quantification of entanglement structures between multiple quantum systems. These techniques will be based on practical requirements, helping to understand complex entanglement structures and connecting these theoretical insights with experimental applicability in current and future quantum technologies. The insights gathered during the project will thus pave the way for a deeper understanding of the complex structures of the quantum systems employed in such devices. If successful, this project will make the developed techniques more widely recognized as useful tools for characterizing quantum devices across various physical platforms, in particular for current machines operating in the so-called noisy intermediate scale regime where noise and errors are still severe limiting factors.