Indefinite causality

Jacquiline Romero, Kaumudikash Goswami, Christina Giarmatzi +4 more

Samuel Fedida, Anne-Catherine de la Hamette, Viktoria Kabel +1 more

We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition. By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant. This reveals an intriguing connection between the field of quantum causality and knot theory. Furthermore, we provide an operational encoding of indefinite causal order and discuss how to incorporate a measure of quantum coherence into our classification.

D. I. Blokhint︠s︡ev

Zhu Cao

Indefinite causal order has found numerous applications in quantum computation, quantum communication, and quantum metrology. Before its usage, the quality of the indefinite causal order needs to be first certified, and the certification should ideally be device independent (DI) to avoid the impact of device imperfections. In this work, we initiate the study of the sequential DI certification of an indefinite causal order. This can be useful in experimental platforms where the generation of an indefinite causal order is difficult. We show that an arbitrary number of sequential DI certifications of an indefinite causal order can be achieved with a quantum switch and also analyze practical requirements for experimental implementations of the certifications. Our work opens the possibility of reusing the resource of an indefinite causal order multiple times in device-independent quantum information processing.

Louis Osgood Kattsoff

Kaumudibikash Goswami, Jacquiline Romero

Quantum causality extends the conventional notion of the fixed causal structure by allowing channels and operations to act in an indefinite causal order. The importance of such an indefinite causal order ranges from the foundational—e.g., towards a theory of quantum gravity—to the applied—e.g., for advantages in communication and computation. In this review, the authors will walk through the basic theory of indefinite causal order and focus on experiments that rely on a physically realizable indefinite causal ordered process—the quantum switch.