Mutually Unbiased Bases and The Complementarity Polytope
| dc.creator | Bengtsson, Ingemar | |
| dc.creator | Ericsson, Asa | |
| dc.date | 2004-10-15 | |
| dc.date.accessioned | 2026-07-07T06:21:33Z | |
| dc.date.available | 2026-07-07T06:21:33Z | |
| dc.description | 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. | |
| dc.description | 18 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0410120 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0410120 | |
| dc.identifier | Open Sys. & Information Dyn. (2005) 12: 107-120 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95635 | |
| dc.subject | Quantum Physics | |
| dc.title | Mutually Unbiased Bases and The Complementarity Polytope | |
| dc.type | text |