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| related topics |
| {let, theorem, proof} |
| {states, state, optimal} |
| {group, space, representation} |
| {theory, mechanics, state} |
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Mutually Unbiased Bases and The Complementarity Polytope
Ingemar Bengtsson, Asa Ericsson
abstract: A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope
in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a
geometrical object such a polytope exists for all values of N, while it is
unknown whether it can be made to lie within the body of density matrices
unless N=p^k, where p is prime. We investigate the polytope in order to see if
some values of N are geometrically singled out. One such feature is found: It
is possible to select N^2 facets in such a way that their centers form a
regular simplex if and only if there exists an affine plane of order N. Affine
planes of order N are known to exist if N=p^k; perhaps they do not exist
otherwise. However, the link to the existence of MUBs--if any--remains to be
found.
- oai_identifier:
- oai:arXiv.org:quant-ph/0410120
- categories:
- quant-ph
- comments:
- 18 pages, 3 figures
- arxiv_id:
- quant-ph/0410120
- journal_ref:
- Open Sys. & Information Dyn. (2005) 12: 107-120
- report_no:
- USITP 04-7
- created:
- 2004-10-15
Full article ▸
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