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CLIFFORD TORI AND UNBIASED VECTORS
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.ORCID iD: 0000-0002-4203-3180
Number of Authors: 22017 (English)In: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 79, no 1, p. 33-51Article in journal (Refereed) Published
Abstract [en]

The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the question whether two Lagrangian Clifford tori intersect, and a body of results exists concerning it. These results are however rather weak from the point of view of the first problem. We make a detailed study of how the intersections behave in the simplest nontrivial case, that of complex projective 2-space (the qutrit), for which the set of pairs of Clifford tori can be usefully parametrized by the unistochastic subset of Birkhoff's polytope. Pairs that do not intersect transversally are located. Some calculations in higher dimensions are included to see which results are special to the qutrit.

Place, publisher, year, edition, pages
2017. Vol. 79, no 1, p. 33-51
Keywords [en]
mutually unbiased bases, Lagrangian submanifolds, Birkhoff's polytope
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-174654DOI: 10.1016/S0034-4877(17)30019-8ISI: 000395211500003OAI: oai:DiVA.org:su-174654DiVA, id: diva2:1359665
Available from: 2019-10-10 Created: 2019-10-10 Last updated: 2019-12-09Bibliographically approved

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Andersson, OleBengtsson, Ingemar
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