Graph state basis for Pauli Channels

TL;DR

This paper presents a graph state basis diagonalization method that significantly accelerates the calculation of coherent information for quantum codes in Pauli channels, aiding in understanding quantum capacity.

Contribution

It introduces a novel graph state basis approach that simplifies and speeds up the analysis of quantum codes passing through Pauli channels, especially for non-additive codes.

Findings

Calculation speed improved by a factor of 5000 for certain codes

Method simplifies the evaluation of quantum capacity

Applicable to non-additive quantum codes

Abstract

We introduce graph state basis diagonalization to calculate the coherent information of a quantum code passing through a Pauli channel. The scheme is 5000 times faster than the best known one for some concatenated repetition codes, providing us a practical constructive way of approaching the quantum capacity of a Pauli channel. The calculation of the coherent information of non-additive quantum code can also be greatly simplified in graph state basis.