Mutually Unbiased Bases and The Complementarity Polytope

dc.creatorBengtsson, Ingemar
dc.creatorEricsson, Asa
dc.date2004-10-15
dc.date.accessioned2026-07-07T06:21:33Z
dc.date.available2026-07-07T06:21:33Z
dc.descriptionA 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.
dc.description18 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0410120
dc.identifierhttp://arxiv.org/abs/quant-ph/0410120
dc.identifierOpen Sys. & Information Dyn. (2005) 12: 107-120
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95635
dc.subjectQuantum Physics
dc.titleMutually Unbiased Bases and The Complementarity Polytope
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