  Certain quantum devices, such as half-wave plates and quarter-wave plates in
quantum optics, are bidirectional, meaning that the roles of their input and
output ports can be exchanged. Bidirectional devices can be used in a forward
mode and a backward mode, corresponding to two opposite choices of the
input-output direction. They can also be used in a coherent superposition of
the forward and backward modes, giving rise to new operations with indefinite
input-output direction. In this work we explore the potential of input-output
indefiniteness for the transfer of classical and quantum information through
noisy channels. We first formulate a model of communication from a sender to a
receiver via a noisy channel used in indefinite input-output direction. Then,
we show that indefiniteness of the input-output direction yields advantages
over standard communication protocols in which the given noisy channel is used
in a fixed input-output direction. These advantages range from a general
reduction of noise in bidirectional processes, to heralded noiseless
transmission of quantum states, and, in some special cases, to a complete noise
removal. The noise reduction due to input-output indefiniteness can be
experimentally demonstrated with current photonic technologies, providing a way
to investigate the operational consequences of exotic scenarios characterised
by coherent quantum superpositions of forward-time and backward-time processes.
