Quantum Correlations in Causal Inference and Applications

Quantum theory has puzzled researchers since the beginnings. This is commonly exemplified by means of the counterintuitive correlations one can observe in quantum mechanical systems, sometimes known as ``spooky action at a distance. While these are nowadays well-understood, we still lack an intuitive physical explanation as to why quantum theory is the way it is. Indeed, the more complex the scenarios we consider, the more we still encounter aspects for which our current understanding of quantum theory is not adequate. One of those aspects is reasoning about cause and effect. This is very central to science and necessary for analysing and understanding the implications of experiments and studies. A common example are medical trials. There, control groups are used in order to infer that the recovery of patients can indeed be attributed to the effect of a drug to be tested. But what can we infer in situations where some of the variables involved in a study or experiment are quantum? With this project, we aim to develop new mathematical tools to infer such causal relations among quantum systems and to describe the experimental observations they can lead to. These tools have many immediate applications, one that is addressed in this project is the analysis of communication over quantum networks. We aim to explain, for instance, how data that is stored in a large quantum database distributed among several parties can be most efficiently recovered by an individual, without being leaked. With the current effort towards setting up large quantum communication networks that will eventually lead to a so-called quantum internet, this type of problem is at the verge of becoming technologically implementable. We further aim to dive into foundational questions. Indeed, there are various classes of theories that lead to similar predictions as quantum theory but that slightly differ from it. Quantum networks give us new ways to compare those theories and to identify features that are special to quantum theory. This allows us, for instance, to design experiments that rule some of those other theories out. In the long run, we aim to identify a specific aspect of quantum theory that allows us to disprove all of those competing theories. This line of research may allow us to finally understand why quantum theory is the way it is.

The study of quantum mechanics has led us to discover various phenomena, such as the existence of entangled quantum systems, which are currently used to build new technologies, for instance quantum computers or new cryptographic devices. The better we understand such quantum systems, the more complicated the experiments and technologies we involve these systems in. In particular, recent progress has led us to develop methods for studying quantum systems in networks. The project ``Quantum Correlations in Causal Inference and Applications'' is in line with these new developments and has demonstrated new ways to use such networks of quantum systems, on the one hand for understanding the foundations of quantum theory, on the other hand for devising new protocols for information processing tasks. Specifically, on the information theory side, we developed new protocols for information processing tasks and ways to optimize such protocols. These include protocols for non-locality distillation and protocols for entanglement certification, among others. Non-locality distillation can be used to facilitating certain information-theoretic tasks, for instance it reduces the communication needed by two parties to perform a computation on data that is distributed between the parties. Entanglement is a resource for many applications, including quantum computation, thus its efficient certification in large quantum systems is currently an important problem. On the foundational side, this project made progress towards singling out quantum theory in a general landscape of physical theories, by devising experiments that allow us to rule out competing theories. The theories we managed to rule out include quantum theory over real Hilbert spaces, which was for a long time believed to make exactly the same predictions as the (usual) quantum theory over complex Hilbert spaces. This research thus solves a long-standing open problem in the foundation of quantum theory in an unexpected way. It furthermore brings us a step closer to identifying the physical principles underlying quantum theory.