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Supermaps are higher-order transformations that take maps as input. We explore quantum algorithms that implement supermaps of unitary operations using multiple calls to a black-box unitary operation. We investigate how the causal structure and spacetime symmetry of these unitary black-boxes affect their performance in implementing higher-order quantum operations. We analyze several tasks, inversion, complex conjugation, and transposition of black-box unitaries.

Generalizations of Bell's theorem, particularly within quantum networks, are now being analyzed through the causal inference lens. However, the use of interventions, a central concept in causality theory, remains unexplored. As will be discussed, if we are not limited to observational data and can intervene in our experimental setup, we can witness quantum violations of classical causal bounds even when no Bell-like violation is possible. Through interventions, the quantum behavior of a system, that would seem classical otherwise, can be demonstrated. We will then present a photonic experiment implementing those ideas and consider applications of this framework for measurement-based quantum computation, quantification of causality in quantum gates and quantum network protocols.

In QFT, one aspect of relativistic causality is the principle of microcausality, which requires that observables associated with spacelike separated regions commute. But this principle is not by itself sufficient to rule out superluminal signalling, as examples of ‘impossible’ measurements demonstrate. Representations of the dynamics that respect relativity also play a necessary role in upholding relativistic causality in QFT. This talk will focus on the important role that principles of relativistic dynamics play in representations of local measurement in QFT.

The notion of causality is intimately tied to both, a transitive ordering on events, and the possibility of unrelated events. Thus, any causality structure is a partially ordered set or poset. This is the case in Lorentzian spacetime, which possesses a single time direction. In causal set quantum gravity, this spacetime causality structure is "first quantised" by discretising it. However, as with any dynamical quantum theory of spacetime, background notions of causality are insufficient. I will discuss how ordering and discreteness, as manifested in the sequential growth paradigm, provide a broad framework for quantum dynamical notions of causality.

There are several non-causal effects that have been attributed to quantum physics. These include the analogues of "closed timelike curve effects" in quantum circuits proposed by David Deutsch (D-CTC), and the "impossible measurements" in relativistic quantum field theory discussed by Raphael Sorkin. Based on previous work, it will be pointed out in the talk that the alleged non-causality features arise not only in quantum systems, but in the very same manner in systems that are described in the framework of classical (non-quantum) statistical mechanics or classical field theory. Therefore, although the said non-causality scenarios have been portrayed as pertaining to quantum systems or quantum fields, they are in fact not based on, nor characteristic of, the quantum nature of physical systems.