Experimental device-independent certification of indefinite causal order

Abstract: Understanding the physical world fundamentally relies on the assumption that events are temporally ordered, with past events serving as causes for future ones. However, quantum mechanics permits events to occur in a superposition of causal orders, providing new types of quantum resources for quantum information tasks. Previous demonstrations of indefinite causal order have relied on a process known as quantum switch and depended on specific assumptions about the devices used in the laboratory. Recently, a theoretical scheme for the certification of indefinite causal order in the quantum switch has been obtained solely from the output statistics of the devices, analogous to the device-independent proofs of nonlocality through violations of the Bell inequality. Here, we report an experimental verification of the causal inequality using spacelike-separated entangled photons, where one photon functions as the control qubit in a quantum switch and the other serves as an additional observer. Through local measurement statistics, we observe a violation of the causal inequality by 24 standard deviations. This work provides evidence for a device-independent certification of indefinite causal order, relying solely on observed correlations without requiring device characterization. Our results pave the way toward a complete understanding of indefinite causal order and its potential applications in quantum information processing.