Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes

TL;DR

This paper demonstrates that entanglement enhances quantum error correction by optimizing code parameters, leading to new codes that reach theoretical bounds, and introduces a random search method for optimization.

Contribution

It introduces an optimization method for entanglement-assisted quantum codes, resulting in new codes that saturate the quantum singleton bound and a random search algorithm for code design.

Findings

New EAQEC codes including [[n, 1, n; n-1]] for odd n

Codes [[7, 1, 5; 2]], [[7, 1, 5; 3]], [[9, 1, 7; 4]], [[9, 1, 7; 5]] saturate the quantum singleton bound

A random search algorithm for encoding optimization

Abstract

If entanglement is available, the error-correcting ability of quantum codes can be increased. We show how to optimize the minimum distance of an entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding ebits to a standard quantum error-correcting code, over different encoding operators. By this encoding optimization procedure, we found several new EAQEC codes, including a family of [[n, 1, n; n-1]] EAQEC codes for n odd and code parameters [[7, 1, 5; 2]], [[7, 1, 5; 3]], [[9, 1, 7; 4]], [[9, 1, 7; 5]], which saturate the quantum singleton bound for EAQEC codes. A random search algorithm for the encoding optimization procedure is also proposed.