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Recently a complete set of entropic conditions has been derived for theinterconversion structure of states under quantum operations that respect aspecified symmetry action, however the core structure of these conditions isstill only partially understood. Here we develop a coarse-grained descriptionwith the aim of shedding light on both the structure and the complexity of thisgeneral problem. Specifically, we consider the degree to which one canassociate a basic `shape' property to a quantum state or channel that capturescoarse-grained data either for state interconversion or for the use of a statewithin a simulation protocol. We provide a complete solution for the two-qubitcase under the rotation group, give analysis for the more general case anddiscuss possible extensions of the approach.

On the classification of two-qubit group orbits and the use of coarse-grained 'shape' as a superselection property