Duality in Entanglement-Assisted Quantum Error Correction
Ching-Yi Lai, Todd A. Brun, and Mark M. Wilde
TL;DR
This paper introduces a duality concept for entanglement-assisted quantum error-correcting codes, deriving bounds and identities that advance understanding of their structure and limitations.
Contribution
It defines the dual of EAQEC codes using orthogonal groups, leading to new MacWilliams identities and bounds on code parameters.
Findings
Derived MacWilliams identities for EAQEC codes
Established bounds on minimum distance for small-length codes
Provided a comprehensive table of code bounds up to 15 qubits
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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