Experimental violation of a Bell-like inequality for causal order

Quantum mechanics allows for coherent control over the order in which different processes take place on a target system, giving rise to a new feature known as indefinite causal order. Indefinite causal order provides a resource for quantum information processing, and can be in principle be detected by the violation of certain inequalities on the correlations between measurement outcomes observed in the laboratory, in a similar way as quantum nonlocality can be detected by the violation of Bell inequalities. Here we report the experimental violation of a Bell-like inequality for causal order using a photonic setup where the order of two optical processes is controlled by a single photon of a polarization-entangled photon pair. Our proof-of-principle demonstration overcomes major technical challenges, including the need of high-speed quantum operations in photonic time-bin encoding, nanosecond synchronization of active optical and electronic elements to meet the target required for spacelike separation, and active temperature stabilization of a Mach-Zehnder interferometer to ensure statistically significant violations. These experimental advances enable a statistically significant violation of the causal inequality, and open up a path towards a device-independent certification of indefinite order of events with uncharacterized quantum devices.