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The calculating of the coherent information is a fundamental step inobtaining the quantum capacity of a quantum channel. We introduce orthogonaland complete code basis to evaluate the coherent information per channel usewhen the input is the maximal mixture of stabilizer codewords. In the codebasis, the output density matrix is diagonal, the joint output of the systemand the auxiliary is block diagonal. The coherent information is worked out bycounting the weights of error operators.

The coherent information of Pauli channels with coded inputs