The nature of causality remains one of the key puzzles in science. In quantum theory, the causal structure is not subject to quantum uncertainty and plays rather a background role. The process matrix formalism (PMF) has introduced indefinite causal structures (ICS) by assuming validity of quantum theory in local laboratories while relaxing the global definite causal order between them. Looking for the possible applications of the PMF has been the subject of growing interest in the scientific community as the PMF could provide communication and computational resources not realizable via standard quantum theory. The main goal of this project is to trace both the foundational and practical sides of the ICS in the PMF. Its central topics put under scrutiny implications of the PMF for thermodynamics and its fundamental laws, the underlying mathematical structure, and further benefits offered by ICS for practical tasks.
If you are interested in a collaboration or need additional information on the project, please do not hesitate to write me at my email. Even if the project had incredibly positive reviews, nowadays only evaluations which are excellent in every item are considered for funding. Therefore, the project is at present on resubmission.