Entanglement-assisted quantum error correction

摘要

We describe a natural generalization of the stabilizer formalism for quantum error correcting codes to produce entanglement-assisted quantum error correction codes (EAQECC). Conventional stabilizer codes correspond to dual-containing classical codes. The codes we describe do not require the self-orthogonality condition. Consequently, any classical code over GF(4) can be used to construct a quantum code as long as entanglement is available between sender and receiver. For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement can be used to enable quantum communication.