2020/03/31 by Nicola Pinzani, Stefano Gogioso
Physics and Astronomy · Computer Science · #quant-ph #cs.LO
paper · pdf · doi:10.4204/eptcs.340.13
published as EPTCS 340, 2021, pp. 256-278 · In Proceedings QPL 2020, arXiv:2109.01534
arxiv created 2021/09/06 · arxiv updated 2021/09/07
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.