Title :
Duality in Entanglement-Assisted Quantum Error Correction
Author :
Ching-Yi Lai ; Brun, Todd A. ; Wilde, Mark M.
Author_Institution :
Electr. Eng. Dept., Univ. of Southern California, Los Angeles, CA, USA
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.
Keywords :
Poisson distribution; linear programming; quantum computing; quantum entanglement; MacWilliams identities; Poisson summation formula; duality; entanglement-assisted quantum error correction; linear programming; maximal-entanglement EAQEC code; orthogonal group; stabilizer group; Educational institutions; Error correction codes; Linear programming; Quantum computing; Quantum entanglement; Silicon; Entanglement-assisted quantum error correction (EAQEC); MacWilliams identity; linear programming bound; quantum dual code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2246274
