General channel capacities from quantum channel-state duality

The quantum channel-state duality permits the characterization of a quantum process through a quantum state, referred to as a Choi state. This characteristic serves as the impetus for the quantum computing paradigm that utilizes Choi states as information sources. In this work, the fundamental theorems regarding quantum channel capacity are proven when Choi states are considered as sources. This achievement enriches the set of capacities associated with quantum channels. Moreover, it gives rise to novel opportunities for the comprehension of superadditivity phenomena and the discovery of new classes of quantum error-correction codes.