Simulating Noncausality with Quantum Control of Causal Orders

Abstract: Logical consistency with free local operations is compatible with non-trivial classical communications, where all parties can be both in each other's past and future - a phenomenon known as noncausality. Noncausal processes, such as the ''Lugano (AF/BW) process'', violate causal inequalities, yet their physical realizability remains an open question. In contrast, the quantum switch - a physically realizable process with indefinite causal order - can only generate causal correlations. Building on a recently established equivalence [Kunjwal and Baumeler, PRL 131, 120201 (2023)] between the SHIFT measurement, which exhibits nonlocality without entanglement, and the Lugano process, we demonstrate that the SHIFT measurement can be implemented using a quantum switch of classical communications in a scenario with quantum inputs. This shows that the structure of the Lugano process can be simulated by a quantum switch and that successful SHIFT discrimination witnesses causal nonseparability rather than noncausality, refuting prior claims. Finally, we identify a broad class of ''superposition of classical communications'' derived from classical processes without global past capable of realizing similar causally indefinite measurements. We examine these results in relation to the ongoing debate on implementations of indefinite causal orders.