General entanglement-assisted quantum error-correcting codes

Understand

Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of pre-existing entanglement between the sender and receiver to boost the rate of transmission.

• It is possible to construct an EAQECC from any classical linear code, unlike standard QECCs which can only be constructed from dual-containing codes.
• Operator quantum error-correcting codes (OQECCs) allow certain errors to be corrected (or prevented) passively, reducing the complexity of the correction procedure.
• We combine these two extensions of standard quantum error correction into a unified entanglement-assisted quantum error correction formalism.