Giving Operational Meaning to the Superposition of Causal Orders

Nicola Pinzani
(University of Oxford)
Stefano Gogioso
(University of Oxford)

In this work, we give rigorous operational meaning to superposition of causal orders. This fits within a recent effort to understand how the standard operational perspective on quantum theory could be extended to include indefinite causality. The mainstream view, that of "process matrices", takes a top-down approach to the problem, considering all causal correlations that are compatible with local quantum experiments. Conversely, we pursue a bottom-up approach, investigating how the concept of indefiniteness emerges from specific characteristics of generic operational theories. Specifically, we pin down the operational phenomenology of the notion of non-classical (e.g. "coherent") control, which we then use to formalise a theory-independent notion of control (e.g. "superposition") of causal orders. To validate our framework, we show how salient examples from the literature can be captured in our framework.

In Benoît Valiron, Shane Mansfield, Pablo Arrighi and Prakash Panangaden: Proceedings 17th International Conference on Quantum Physics and Logic (QPL 2020), Paris, France, June 2 - 6, 2020, Electronic Proceedings in Theoretical Computer Science 340, pp. 256–278.
Published: 6th September 2021.

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