  The essence of quantum error-correction is to use redundant Hilbert space to
identify and correct errors, and the channel fidelity of the quantum channel
does not affect which errors can be identified and corrected. Based on this, it
is found that quantum error-correction can be used to classify the independent
quantum channel into 5 types, and 4 of the 5 types can be purified. It is found
in quantum error-correction, the decoherence of quantum state may be related to
the degree of identification for the state under quantum noise, and the results
of this work confirmed that the degree of purity of quantum channel determines
its ability to retain the quantum property of the quantum state, not the
fidelity. In this work, the identification of the independent Pauli channels by
quantum error-correction is demonstrated.
