Linear Plotkin bound for entanglement-assisted quantum codes

The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform arbitrary quaternary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entanglement between the sender and the receiver. Using the special structure of linear EAQECCs, we derive an EA-Plotkin bound for linear EAQECCs, which strengthens the previous known EA-Plotkin bound. This linear EA-Plotkin bound is tighter then the EA-Singleton bound, and matches the EA-Hamming bound and the EA-linear programming bound in some cases. We also construct three families of EAQECCs with good parameters. Some of these EAQECCs saturate this linear EA-Plotkin bound and the others are near optimal according to this bound; almost all of these linear EAQECCs are degenerate codes. DOI: 10.1103/PhysRevA.87.032309