  Recent work has shown how to use the laws of quantum mechanics to keep
classical and quantum bits secret in a number of different circumstances. Among
the examples are private quantum channels, quantum secret sharing and quantum
data hiding. In this paper we show that a method for keeping two classical bits
hidden in any such scenario can be used to construct a method for keeping one
quantum bit hidden, and vice--versa. In the realm of quantum data hiding, this
allows us to construct bipartite and multipartite hiding schemes for qubits
from the previously known constructions for hiding bits. Our method also gives
a simple proof that two bits of shared randomness are required to construct a
private quantum channel hiding one qubit.
