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Causal nonseparability is the property underlying quantum processesincompatible with a definite causal order. So far it has remained a centralopen question as to whether any process with a clear physical realisation canviolate a causal inequality, so that its causal nonseparability can becertified in a device-independent way, as originally conceived. Here we presenta method solely based on the observed correlations, which certifies the causalnonseparability of all the processes that can induce a causally nonseparabledistributed measurement in a scenario with trusted quantum input states, asdefined in [Dourdent et al., Phys. Rev. Lett. 129, 090402 (2022)]. This notablyincludes the celebrated quantum switch. This device-independent certificationis achieved by introducing a network of untrusted operations, allowing one toself-test the quantum inputs on which the effective distributed measurementinduced by the process is performed.

Network-Device-Independent Certification of Causal Nonseparability