Nitica Sakharwade - How models of Indefinite Causality can be understood within Causaloid Framework

Abstract - Towards the studies of Indefinite Causality from a post-quantum lens, a few frameworks have been proposed and studied. The Process Matrix Framework is one such framework that generalises quantum channels to process matrices. This framework has been vastly studied due to the direct applicability of known quantum information tools. Another framework, that chronologically preceded the process matrices is the Causaloid Framework which starts from a more general starting point and can be thought of as incorporating Generalised Probability Theories as well as Indefinite Causality. The Framework has been worked on more recently to be made more accessible. Further a hierarchy within the Causaloid Framework that is distinct from Sorkin's hierarchy, that depends on composition has been introduced. A natural question arises as to how the Process Matrix Formalism and the Causaloid Framework are related and how they can be understood through the introduced hierarchy. We answer this question by showing how the bipartite Process Matrices are a special instance in the Causaloid Framework. This work helps fill a theoretical gap in the literature and by understanding Indefinite Causality from the lens of Generalised Probability Theories helps us make attempts towards an axiomatic approach to Indefinite Causality. Based on N. Sakharwade, An Operational Road towards Understanding Causal Indefiniteness within Post-Quantum Theories, 2022 and ongoing work.

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