  We make an explicit connection between fundamental notions in quantum
cryptography and quantum error correction. Error-correcting subsystems (and
subspaces) for quantum channels are the key vehicles for contending with noise
in physical implementations of quantum information-processing. Private
subsystems (and subspaces) for quantum channels play a central role in
cryptographic schemes such as quantum secret sharing and private quantum
communication. We show that a subsystem is private for a channel precisely when
it is correctable for a complementary channel. This result is shown to hold
even for approximate notions of private and correctable defined in terms of the
diamond norm for superoperators.
