  Quantum theory is compatible with scenarios in which the order of operations
is indefinite. Experimental investigations of such scenarios, all of which have
been based on a process known as the quantum switch, have provided
demonstrations of indefinite causal order conditioned on assumptions on the
devices used in the laboratory. But is a device-independent certification
possible, similar to the certification of Bell nonlocality through the
violation of Bell inequalities? Previous results have shown that the answer is
negative if the switch is considered in isolation. Here, however, we present an
inequality that can be used to device-independently certify indefinite causal
order in the quantum switch in the presence of an additional
spacelike-separated observer under an assumption asserting the impossibility of
superluminal and retrocausal influences.
