  A quantum process encodes the causal structure that relates quantum
operations performed in local laboratories. The process matrix formalism
includes as special cases quantum mechanics on a fixed background space-time,
but also allows for more general causal structures. Motivated by the
interpretation of processes as a resource for quantum information processing
shared by two (or more) parties, with advantages recently demonstrated both for
computation and communication tasks, we investigate the notion of composition
of processes. We show that under very basic assumptions such a composition rule
does not exist. While the availability of multiple independent copies of a
resource, e.g. quantum states or channels, is the starting point for defining
information-theoretic notions such as entropy (both in classical and quantum
Shannon theory), our no-go result means that a Shannon theory of general
quantum processes will not possess a natural rule for the composition of
resources.
