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Entanglement-assisted quantum error-correcting codes over arbitrary finite fields (1812.05312v4)
Published 13 Dec 2018 in cs.IT, math.IT, and quant-ph
Abstract: We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as well. We also give a Gilbert-Varshamov bound for EAQECCs and constructions of EAQECCs coming from punctured self-orthogonal linear codes which are valid for any finite field.