The quantum communication power of indefinite causal order

Abstract: Quantum theory is in principle compatible with scenarios where physical processes take place in an indefinite causal order, a possibility that was shown to yield advantages in several information processing tasks. However, advantages in communication, the most basic form of information processing, have so far remained controversial and hard to prove. Here we develop a framework that can be used to rigorously assess the role of causal order in a scenario where communication links are built by assembling multiple quantum devices. In this setting, we establish a clear-cut advantage of indefinite order in the one-shot transmission of classical messages. On the other hand, we also show that the advantage is not generic to all communication tasks. Notably, we find that indefinite order does not offer any advantage over shared entanglement in the asymptotic scenario where a large number of uses of the same communication device is employed. Overall, our results unveil non-trivial relations between communication, causal order, entanglement, and no-signaling resources in quantum mechanics.