  Quantum mechanics allows for situations where the relative order between two
processes is entangled with a quantum degree of freedom. Here we show that such
entanglement can enhance the ability to transmit quantum information over noisy
communication channels. We consider two completely dephasing channels, which in
normal conditions are unable to transmit any quantum information. We show that,
when the two channels are traversed in an indefinite order, a quantum bit sent
through them has a 25% probability to reach the receiver without any error. For
partially dephasing channels, a similar advantage takes place
deterministically: the amount of quantum information that can travel through
two channels in a superposition of orders can be larger than the amount of
quantum information that can travel through each channel individually.
