On pure MDS asymmetric entanglement-assisted quantum error-correcting codes

TL;DR

This paper characterizes pure MDS asymmetric entanglement-assisted quantum error-correcting codes by analyzing linear l-intersection pairs of MDS codes, providing a complete classification for all parameters.

Contribution

It offers a complete characterization of pure MDS AEAQECCs by analyzing linear l-intersection pairs of MDS codes, a novel approach in quantum error correction.

Findings

All possible linear l-intersection pairs of MDS codes are classified.

A complete characterization of pure MDS AEAQECCs for all parameters is provided.

The relationship between code intersection dimensions and entanglement requirements is clarified.

Abstract

Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting codes (AEAQECCs) from Calderbank-Shor-Steane (CSS) construction. In general, it's difficult to determine the required number of maximally entangled states of an AEAQECC, which is associated with the dimension of the intersection of the two corresponding linear codes. Two linear codes are said to be a linear l-intersection pair if their intersection has dimension l. In this paper, all possible linear l-intersection pairs of MDS codes are given. As an application, we give a complete characterization of pure MDS AEAQECCs for all possible parameters.