Covariant feedback Control of arbitrary qudit state against Depolarizing Noise is impossible

In this paper, we prove that it is impossible to construct a convariant quantum feedback control instruments which aim to correct the channel noise imposed on an unknown qubit. The proof is based on the searching for the optimal quantum control protocol and it turns out there exist no better %\textit{Complete Positive Trace %Preserving}(CPTP) maps complete positive and covariant quantum operations which provide a higher fidelity than the trivial Identity operators. The generalization of the investigation to bipartite entangled pure state is also included.