Entanglement-assisted quantum error-correcting codes from units

Abstract

Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate R, required error-correcting capability to correct t errors, mds (maximum distance separable) EAQECCs of the form [[n, r, d; c]] with R = r n , d ≥ (2t + 1), c = (n − r), d = (n − r + 1) are constructed. Series of such codes may be constructed where the rate and the relative distance approach non-zero constants as n approaches infinity. The codes may also be constructed over prime order fields in which modular arithmetic may be employed.

Maximum distance separable codes to order

“…This is further developed for the construction and development of Entanglement assisted quantum error-correcting codes, EAQECC, of different types and to required specifications in [8].…”