A family of quantum protocols

We introduce three new quantum protocols involving noisy quantum channels and entangled states, and relate them operationally and conceptually with four well-known old protocols. Two of the new protocols (the mother and father) can generate the other five child protocols by direct application of teleportation and superdense coding, and can be derived in turn by making the old protocols coherent. This gives very simple proofs for two famous old protocols (the hashing inequality and quantum channel capacity) and provides the basis for optimal trade-off curves in several quantum information processing tasks.