01144nas a2200157 4500008004100000245005200041210004800093260001400141300001400155490000700169520070100176100002400877700002300901700001800924856004400942 2007 eng d00aThe limitations of nice mutually unbiased bases0 alimitations of nice mutually unbiased bases c2006/7/11 a111 - 1230 v253 a Mutually unbiased bases of a Hilbert space can be constructed by partitioning
a unitary error basis. We consider this construction when the unitary error
basis is a nice error basis. We show that the number of resulting mutually
unbiased bases can be at most one plus the smallest prime power contained in
the dimension, and therefore that this construction cannot improve upon
previous approaches. We prove this by establishing a correspondence between
nice mutually unbiased bases and abelian subgroups of the index group of a nice
error basis and then bounding the number of such subgroups. This bound also has
implications for the construction of certain combinatorial objects called nets.
1 aAschbacher, Michael1 aChilds, Andrew, M.1 aWocjan, Pawel uhttp://arxiv.org/abs/quant-ph/0412066v1