  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.
