  When classical or quantum information is broadcast to separate receivers,
there exist codes that encrypt the encoded data such that the receivers cannot
recover it when performing local operations and classical communication, but
they can decode reliably if they bring their systems together and perform a
collective measurement. This phenomenon is known as quantum data hiding and
hitherto has been studied under the assumption that noise does not affect the
encoded systems. With the aim of applying the quantum data hiding effect in
practical scenarios, here we define the data-hiding capacity for hiding
classical information using a quantum channel. Using this notion, we establish
a regularized upper bound on the data hiding capacity of any quantum broadcast
channel, and we prove that coherent-state encodings have a strong limitation on
their data hiding rates. We then prove a lower bound on the data hiding
capacity of channels that map the maximally mixed state to the maximally mixed
state (we call these channels "mictodiactic"---they can be seen as a
generalization of unital channels when the input and output spaces are not
necessarily isomorphic) and argue how to extend this bound to generic channels
and to more than two receivers.
