A. R. Calderbank, E. M Rains, P. W. Shor, N. J. A. Sloane
Published 1996-08-06, updated 1997-09-10Version 5
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.
Comments: Latex, 46 pages. To appear in IEEE Transactions on Information Theory. Replaced Sept. 24, 1996, to correct a number of minor errors. Replaced Sept. 10, 1997. The second section has been completely rewritten, and should hopefully be much clearer. We have also added a new section discussing the developments of the past year. Finally, we again corrected a number of minor errors
Separability and lower bounds of quantum entanglement based on realignment
Sufficient conditions, lower bounds and trade-off relations for quantumness in Kirkwood-Dirac quasiprobability
Lower Bounds of Entanglement Quantifiers Based On Entanglement Witnesses
