Michael H. Freedman and David A. Meyer, with an appendix by Feng Luo,
``Z₂-systolic freedom and quantum codes'',
in Ranee K. Brylinski and Goong Chen, eds.,
The Mathematics of Quantum Computation
(Boca Raton: CRC Press 2002) 287-320.

A closely coupled pair of conjectures/questions--one in differential geometry (by M. Gromov), the other in quantum information theory--are both answered in the negative. The answer derives from a certain metrical flexibility of manifolds and a corresponding improvement to the theoretical efficiency of existing local quantum codes. We exhibit this effect by constructing a family of metrics on S² x S¹, and other three and four dimensional manifolds. Quantitatively, the explicit ``freedom'' exhibited is too weak (a log^1/2 factor in the natural scaling) to yield practical codes but we cannot rule out the possibility of other families of geometries with more dramatic freedom.

Not available online.