MUBs inequivalence and affine planes

Details MUBs inequivalence and affine planes MUBs inequivalence and affine planes

2011-04-18

arxiv.org/abs/1104.3370v3

Mathematics

Combinatorics

This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the

Scientific paper

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.

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