Three new classes of entanglement-assisted quantum MDS codes from generalized Reed–Solomon codes.

Entanglement-assisted quantum error-correcting (EAQEC) codes can be obtained from arbitrary classical linear codes, based on the entanglement-assisted stabilizer formalism. However, how to determine the required number of shared pairs is challenging. In this paper, we first construct three classes of classical linear MDS codes over finite fields by considering generalized Reed–Solomon codes and calculate the dimension of their Hermitian hulls. By using these MDS codes, we then obtain three new classes of EAQEC codes and EAQEC MDS codes, whose maximally entangled states can take various values. Moreover, these EAQEC codes have more flexible lengths. [ABSTRACT FROM AUTHOR]