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arXiv · 1302.4150

Duality in Entanglement-Assisted Quantum Error Correction

Ching-Yi Lai·Todd A. Brun·Mark M. Wilde
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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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Ching-Yi Lai, Todd A. Brun, Mark M. Wilde. 2013-02-18. Duality in Entanglement-Assisted Quantum Error Correction. https://doi.org/10.1109/tit.2013.2246274

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