Spatial modes for testing indefinite causal order

The fundamental notion of fixed order between two events is challenged by formulations of quantum mechanics that makes no reference to a global time. The indefinite causal order arising from these formalisms can be realised using the quantum switch, a device where two operations can act in two different orders simultaneously. Similar to entanglement verification which employ entanglement witness, we verify indefinite causal order using a causal witness. In our experiment, we use polarisation as a control for the order of the operations that act on the spatial mode of a photon. We measure a causal witness value of -0.16±0.013, below the threshold of zero, thus demonstrating indefinite causal order in the quantum switch.