MUBs, Polytopes, and Finite Geometries

Ingemar Bengtsson
<span title="">2005</span> <i title="AIP"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3jzz7zp4afbbpdcvegp6zk7rp4" style="color: black;">AIP Conference Proceedings</a> </i> &nbsp;
A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes. I explore the question whether the existence of complete sets of MUBs is directly related to the existence of finite affine planes. Both questions can be shown to be geometrical
more &raquo; ... questions about a convex polytope, but not in any obvious way the same question.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.1874558">doi:10.1063/1.1874558</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b27gblxyhzeo7owpkfkfm7a4p4">fatcat:b27gblxyhzeo7owpkfkfm7a4p4</a> </span>
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