Classically, no information can be transmitted through a depolarising, which is a completely noisy, channel. We show that by combining a depolarising channel with another channel in an indefinite causal order—that is, when there is a superposition of the order that these two channels were applied—it becomes possible to transmit significant information. We consider two limiting cases. When both channels are fully depolarising, the ideal limit is communication of 0.049 bits; experimentally we achieve (3.4 ± 0.2) × 10−2 bits. When one channel is fully depolarising, and the other is a known unitary, the ideal limit is communication of 1 bit. We experimentally achieve 0.64 ± 0.02 bits. Our results offer intriguing possibilities for future communication strategies beyond conventional quantum Shannon theory.