In this talk I'll discuss work that shows basic notions in quantum cryptography and quantum error correction are complementary to each other. Error-correcting codes for quantum channels (represented by completely positive maps) are the key vehicles used to avoid noise such as decoherence in quantum information processing. Private codes for quantum channels play a central role in the development of private quantum communication networks designed to prevent adversarial attacks by eavesdroppers. It turns out that a code is private for a channel precisely when it is correctable for a complementary channel, and there is a straightforward algebraic recipe that enables movement between the two perspectives. Moreover, an approximate version of the relationship can be quantified in terms of diamond (or completely bounded) norms for channels.

I'll begin with an introductory look at the two notions then formulate the main result. This talk is based on joint work with Dennis Kretschmann (TU Braunschweig) and Robert Spekkens (Cambridge).