Quanten-Kausalität: Mathematische und praktische Aspekte

Wider research context/theoretical framework: it is well known that causality plays a fundamental role in our everyday life: in fact, the causal nature of our actions is one of the first things a newborn brain has to learn about. However, the fundamental status of causality remains a subject of debates and one of the key puzzles in physics and philosophy. In quantum theory, the causal structure is not subject to quantum uncertainty and plays a background role rather. This conflicts with non-local correlations allowed by quantum theory and might be at the origin of difficulties with the unification of quantum theory with general relativity. It is questioned whether the underlying causal structure can be dropped, for example, by assuming a local causal structure only. This idea was recently formalized within process matrix formalism describing mathematically the situations when the causal order of events is not definite.

Hypotheses/research questions/objectives: looking for the possible applications of process matrix formalism has been the subject of growing interest in the scientific community as process matrix formalism could provide communication and computational resource not realizable via standard quantum theory. The main objective of the present research project is to provide new insights into the fundamental impact of process matrix formalism and address some practical benefits of indefinite causal structures.

Approach/methods: I intend a systematic study of mathematical and practical aspects of quantum theory on indefinite causal structures using process matrix formalism and plan to demonstrate causal non-separability as a valuable resource in a wide range of operational tasks. To this aim, I plan to approach by addressing thermodynamic framework within the process matrix formalism and its fundamental laws, characterization of causal non-separability using machine learning, and finding new applications of causal non-separability to thermodynamic protocols and information processing.

Level of originality/innovation: despite high interest in the potential benefits of indefinite causal structures, the applications of process matrix formalism beyond the quantum switch model and its fundamental aspects are still poorly studied. Via the novel thermodynamic framework, the present research proposal will provide an essential insight into the place of causality in physics. It will fill the gap between the protocols considered so far in the literature and the rich spectrum of causally non-separable resources and shed light on the latter as a valuable resource. The applications of machine learning to indefinite causal structures will be addressed for the first time in the literature.

Primary researchers involved: the principal investigator of the present research project is Kyrylo Simonov, the cooperations include Giulio Chiribella, Veronika Baumann, Lajos Diósi, Philipp Grohs, Tamás Kozsik, Markus Müller, Lee Rozema, Zoltán Zimborás.