Information flow and error scaling for fully quantum control

The optimally designed control of quantum systems is playing an increasingly important role to engineer novel and more efficient technologies. Here, in the scenario represented by controlling arbitrary system via interaction with another initialized auxiliary system, we show that channel capacity sets scaling behaviour optimal error. Specifically, prove minimum error ensured maximizing mapping initial state into target controlled i.e., optimizing information flow from controller be controlled. Analytical results, supported numerical evidences, are provided when either qubits or single Bosonic modes can applied a very large class platforms for controllable devices.