Increasing communication capacity via superposition of order

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) x 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.