Entanglement-assisted quantum error-correcting codes from units
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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.
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