Indefinite causal order in quantum mechanics

Abstract

One of the most deeply rooted concepts in science is causality: the idea that events in the present are caused by events in the past and, in turn, act as causes for what happens in the future. If an event A is a cause of an effect B, then B cannot be a cause of A. Recently we proposed a framework that assumes that operations in local laboratories are described by quantum mechanics, but where no reference is made to any global causal relations between these operations. The central notion of the formalism is “process” which is a generalization of the causal notion of “quantum state”. The framework allows for processes in which two operations are neither causally ordered nor in a probabilistic mixture of definite causal orders, i.e. one cannot say that A is before or after B. However a physical interpretation of such correlations was lacking. I will show that the “superposition of quantum circuits” – in which the gate ordering is not fixed but controlled by a quantum system – is an example of a process with indefinite causal order. This process provides a reduction in query complexity of certain computational problems and can be realized by placing the laboratories in the gravitational field of a massive object in a spatial superposition.