Caslav Brukner, Institute for Quantum Computing (IQC)
Abstract
In quantum physics it is standardly assumed that the background time or definite causal structure exists such that every operation is either in the future, in the past or space-like separated from any other operation. Consequently, the correlations between operations respect definite causal order: they are either signalling correlations for the time-like or no-signalling correlations for the space-like separated operations. We develop a framework that assumes only that operations in local laboratories are described by quantum mechanics (i.e. are completely-positive maps), but relax the assumption that they are causally connected. Remarkably, we find situations where two operations are neither causally ordered nor in a probabilistic mixture of definite causal orders, i.e. one cannot say that one operations is before or after the other. The correlations between the operations are shown to enable performing a communication task ("causal game") that is impossible if the operations are ordered according to a fixed background time.