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The essence of quantum error-correction is to use redundant Hilbert space toidentify and correct errors, and the channel fidelity of the quantum channeldoes not affect which errors can be identified and corrected. Based on this, itis found that quantum error-correction can be used to classify the independentquantum channel into 5 types, and 4 of the 5 types can be purified. It is foundin quantum error-correction, the decoherence of quantum state may be related tothe degree of identification for the state under quantum noise, and the resultsof this work confirmed that the degree of purity of quantum channel determinesits ability to retain the quantum property of the quantum state, not thefidelity. In this work, the identification of the independent Pauli channels byquantum error-correction is demonstrated.

Classification and purification for the independent quantum channel through quantum error-correction