Quantum causality: Mathematical und practical aspects

The fundamental role of causality shaping our everyday life is well known. In fact, one of the first things we learn about in early childhood is the causal nature of our actions: after spending some time with a toy we discover that it makes sound when pressing the button. The concept of causality is, therefore, deeply rooted in our worldview and naturally became one of the major figures in numerous disciplines including philosophy and physics. However, its fundamental status still remains puzzling and debatable. In physics, the infamous difficulties in unification of quantum theory and general relativity might arise from the very notions of causality and time. Quantum theory itself, one of the most successful theories in physics, attributes to them rather a background role, so that causal relations between events (for example, A precedes B) are well-defined from the beginning. On the other hand, quantum theory suggests that a physical system can exist simultaneously in more than one state: this property is known as the superposition principle. A new unified theory might require endowing causal relations with this bizarre quantum property that makes causal order of events indefinite. Such indefinite causal structures, where events A precedes B and B precedes A are true at the same time, can be introduced into the framework of quantum theory by the machinery of process matrix formalism. Moreover, an indefinite causal order of operations can be implemented within present technology in a setup known as the quantum SWITCH. This has immediately launched a research program on information processing tasks featuring indefinite causal structures. Nevertheless, despite the rapidly growing interest in practical benefits of indefinite causal structures, their foundational issues on the borderline with adjacent branches of physics remain underexplored. The proposed research project aims at providing new insights to the impact of indefinite causal structures in process matrix formalism on the fundamental laws of nature and demonstration of indefinite causality as a valuable resource for practical tasks. Therefore, the outcomes of the project will shed light on the very mechanism behind increasing effectiveness of the already known protocols which could be attributed to indefinite causal structures. In turn, it will provide novel applications of indefinite causal structures to information processing and beyond it .