Causal order as a resource for quantum communication

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal uncertainty in the causal order forbids asymptotic quantum communication, while still enabling the noisy transfer of classical information. Therefore causal order, like shared entanglement, is an additional resource for communication. The result is formulated within an asymptotic setting for processes with no fixed causal order, which sets a basis for a quantum information theory in general quantum causal structures.Comment: 5 pages, 1 figur

Integration by differentiation: new proofs, methods and examples

Recently, new methods were introduced which allow one to solve ordinary integrals by performing only derivatives. These studies were originally motivated by the difficulties of the quantum field theoretic path integral, and correspondingly, the results were derived by heuristic methods. Here, we give rigorous proofs for the methods to hold on fully specified function spaces. We then illustrate the efficacy of the new methods by applying them to the study of the surprising behavior of so-called Borwein integrals.Comment: Match published versio