Two class of entanglement-assisted quantum codes from shortened hamming codes

Abstract

Entanglement-assisted quantum error-correcting codes are not only theoretically interesting, but also of great importance in practical physically applications. In this work, two class of entanglement-assisted quantum codes are constructed. The first class of entanglement-assisted quantum codes is minimal ebits entanglement-assisted quantum codes, which require only one copy of maximally entangled state no matter how large the code length is. The second class of entanglement-assisted quantum codes is maximal entanglement entanglement-assisted quantum codes, which can achieve the entanglement-assisted hashing bound asymptotically.