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

Ching-Yi Lai and Todd Brun ∗ 

October 8, 2018 

## 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. 

Index terms: quantum error-correcting codes, quantum stabilizer codes, entanglement-assisted quantum error-correcting codes. 

