Asymptotics of the quantum Hamming bound for subsystem codes

Details Asymptotics of the quantum Hamming bound for subsystem codes Asymptotics of the quantum Hamming bound for subsystem codes

2007-10-23

arxiv.org/abs/0710.4271v1

Physics

Quantum Physics

2 pages

Scientific paper

Ashikhmin and Litsyn showed that all binary stabilizer codes - pure or impure - of sufficiently large length obey the quantum Hamming bound, ruling out the possibility that impure codes of large length can outperform pure codes with respect to sphere packing. In contrast we show that impure subsystem codes do not obey the quantum Hamming bound for pure subsystem codes, not even asymptotically. We show that there exist arbitrarily long Bacon-Shor codes that violate the quantum Hamming bound.

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