The coherent information of Pauli channels with coded inputs

TL;DR

This paper introduces a method to compute the coherent information of Pauli channels with coded inputs using a specialized code basis, simplifying calculations by exploiting the structure of stabilizer codes.

Contribution

It presents a novel approach employing orthogonal and complete code bases to evaluate coherent information for stabilizer code inputs in Pauli channels.

Findings

Coherent information can be efficiently calculated using error operator weights.

The method simplifies the output density matrix to a diagonal form in the code basis.

The approach facilitates analysis of quantum channel capacities with stabilizer codes.

Abstract

The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is the maximal mixture of stabilizer codewords. In the code basis, the output density matrix is diagonal, the joint output of the system and the auxiliary is block diagonal. The coherent information is worked out by counting the weights of error operators.