  Classically, no information can be transmitted through a depolarising, that
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 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
$(3.4{\pm}0.2){\times}10^{-2}$ 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${\pm}$0.02 bits. Our results offer intriguing
possibilities for future communication strategies beyond conventional quantum
Shannon theory.
