Strict Hierarchy between Parallel, Sequential, and Indefinite-Causal-Order Strategies for Channel Discrimination

Funding

We are thankful to Alastair Abbott and Simon Milz for interesting discussions and to Mateus Araujo, Nicolai Friis, and Cyril Branciard for comments on the manuscript. J. B. acknowledges the Austrian Science Fund (FWF) through the START Project No. Y879-N27 and the Zukunftskolleg Project No. ZK03. M. M. is supported by the MEXT Quantum Leap Flagship Program (MEXT QLEAP) Grants No. JPMXS0118069605 and No. JPMXS0120351339 and by the Japan Society for the Promotion of Science (JSPS) through KAKENHI Grants No. 17H01694, No. 18H04286, and No. 21H03394. M. T. Q. acknowledges the Austrian Science Fund (FWF) through the SFB project BeyondC (Subproject No. F7103), a grant from the Foundational Questions Institute (FQXi) as part of the Quantum Information Structure of Spacetime (QISS) Project (qiss.fr). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. This project has received funding from the European Unions Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 801110. It reflects only the authors' view; the EU Agency is not responsible for any use that may be made of the information it contains. The Erwin Schrodinger Center for Quantum Science & Technology (ESQ) has received funding from the Austrian Federal Ministry of Education, Science and Research (BMBWF).