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Duality in Entanglement-Assisted Quantum Error Correction
Published 18 Feb 2013 in quant-ph, cs.IT, and math.IT | (1302.4150v1)
Abstract: The dual of an entanglement-assisted quantum error-correcting (EAQEC) code is defined from the orthogonal group of a simplified stabilizer group. From the Poisson summation formula, this duality leads to the MacWilliams identities and linear programming bounds for EAQEC codes. We establish a table of upper and lower bounds on the minimum distance of any maximal-entanglement EAQEC code with length up to 15 channel qubits.
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