Toward an Experimental Device-Independent Verification of Indefinite Causal Order

In classical physics, events follow a definite causal order: the past influences the future, but not the reverse. Quantum theory, however, permits superpositions of causal orders—the so-called indefinite causal orders (ICOs)—which can provide operational advantages over classical scenarios. Verifying such phenomena has sparked significant interest, much like earlier efforts devoted to refuting local realism and confirming quantum entanglement. To date, demonstrations of ICO have all been based a process called the quantum switch and have relied on device-dependent or semi-device-independent protocols. Achieving a device-independent verification of ICO would imply that nature allows for correlations that do not respect causality, independent of any experimental assumptions or underlying theoretical description of the experiment. To this end, a recent theoretical development introduced a Bell-like inequality that allows for fully device-independent verification of ICO in a quantum switch. Here we implement this verification by experimentally violating this inequality. In particular, we measure a value of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>1.8328</a:mn> <a:mo>±</a:mo> <a:mn>0.0045</a:mn> </a:math> , which is 18 standard deviations above the definite causal order bound of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mn>1.75</c:mn> </c:math> . Our work presents the first implementation of a device-independent protocol to verify ICO, albeit in the presence of experimental loopholes. This represents an important step toward the device-independent verification of an ICO and provides a context in which to identify loopholes specifically related to the verification of ICO.