A family of quantum protocols

Quantum protocols, in the conversion of a noisy quantum channel between two spatially separated parties into a noiseless one, were discussed. Basic protocols for each members of the noiseless resource were considered and organized into two mutually dual hierarchies. These basic protocols are suggested to provide the crucial ingredients for constructing optimal protocols and two dimensional trade-offs. It was shown that just as Shannon's capacity theorem can be thought of demonstrating the ability to convert a noisy classical channel at an asymptotic conversion rate equal to the channel's capacity, it is possible to give asymptotic meaning to inequalities between other resources with entropic quantities as coefficients.