Abstract

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.

Key points

• An indefinite causal order (ICO) is a situation wherein the order of different events or operations is placed in a quantum superposition. Thus one cannot ascribe a definite order to these operations.
• The best-studied process with an ICO is the quantum switch, which applies a set of quantum gates in a superposition of all possible permutations. The quantum switch has been experimentally implemented using various degrees of freedom encoded in single photons.
• There is a strong analogy between processes with an ICO and entangled states. This analogy can be used to design techniques to certify ICO.
• The quantum switch can be used to achieve advantages that go beyond devices that can be described by the quantum circuit model. Although there is no general computational advantage from the quantum switch, there are many specific applications, including quantum computation protocols, quantum communication, quantum metrology and even quantum thermodynamics

• L. A. Rozema, T. Strömberg, H. Cao, B.- H. Liu, P. Walther,
  Experimental aspects of indefinite causal order in quantum mechanics
  Nature Review Physics (2024).