Experimental aspects of indefinite causal order in quantum mechanics

In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics and general relativity, these causally indefinite processes have been shown to offer advantages in a wide variety of quantum-information processing tasks, ranging from quantum computation to quantum metrology. Here, we overview these advantages and the experimental efforts to realize them. We survey both the experimental techniques employed and the theoretical methods developed in support of the experiments, before discussing the interpretations of current experimental results and giving an outlook on the future of the field. Quantum superpositions of orders of operations can be used to create an indefinite causal order. This Review covers experimental implementations of such processes, focusing on characterization techniques, and discusses their applications and limitations.