arXiv:1008.2598v2 [quant-ph] 13 Sep 2010 Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes October 8, 2018 Ching-Yi Lai and Todd Brun ∗ 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. ∗ The authors are with the Communication Sciences Institute of the Ming Hsieh Electrical Engineering Department, University of Southern California, Los Angeles, CA 90089, USA (E-mails: laiching@usc.edu and tbrun@usc.edu) 1 Index terms: quantum error-correcting codes, quantum stabilizer codes, entanglement-assisted quantum error-correcting codes.