Constructions of q-ary entanglement-assisted quantum MDS codes with minimum distance greater than q + 1

TL;DR

This paper introduces five new classes of entanglement-assisted quantum MDS codes with minimum distances exceeding traditional bounds, leveraging classical MDS codes and pre-shared entanglement.

Contribution

The paper constructs five classes of EAQMDS codes with larger minimum distances than standard quantum MDS codes, some requiring only one entangled pair.

Findings

Codes have larger minimum distance than standard QMDS codes

Three classes use only one entangled pair

Codes are based on classical MDS codes

Abstract

The entanglement-assisted stabilizer formalism provides a useful framework for constructing quantum error-correcting codes (QECC), which can transform arbitrary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this paper, we construct five classes of entanglement-assisted quantum MDS (EAQMDS) codes based on classical MDS codes by exploiting one or more pre-shared maximally entangled states. We show that these EAQMDS codes have much larger minimum distance than the standard quantum MDS (QMDS) codes of the same length, and three classes of these EAQMDS codes consume only one pair of maximally entangled states.