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QI: Fachverband Quanteninformation
QI 39: Quantum Foundations
QI 39.7: Vortrag
Freitag, 14. März 2025, 12:30–12:45, HS VIII
Correlations and quantum circuits with dynamical causal order — •Raphaël Mothe1,2,3, Alastair Abbott3, and Cyril Branciard1 — 1Institut Néel, CNRS, Grenoble, France — 2University of Siegen, Siegen, Germany — 3Inria, Grenoble, France
Requiring that the causal structure between different parties is well-defined imposes constraints on the correlations they can establish, which define so-called causal correlations. Some of these are known to be dynamical in that their causal structure is not fixed a priori but is instead established on the fly, with for instance the causal order between future parties depending on some choice of parties in the past. Here we identify a new way that the causal order between the parties can be dynamical: with at least four parties, there can be some dynamical order, which can nevertheless not be influenced by the choice of past parties. This leads us to introduce an intermediate class of correlations with what we call non-influenceable causal order, in between the set of non-dynamical correlations and the set of general causal correlations. We then define analogous classes of processes, considering the recently introduced classes of quantum circuits with classical or quantum control of causal order the latter being the largest class within the process matrix formalism known to have a clear interpretation in terms of coherent superpositions of causal orders. This allows us to formalise precisely in which sense certain quantum processes can have both indefinite and dynamical causal orders.
Keywords: Quantum causality; Indefinite causal order