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Mutually unbiased bases, Heisenberg-Weyl orbits and the distance between them
Stockholm University, Faculty of Science, Department of Physics.
2012 (English)Conference paper (Other academic)
Abstract [en]

There is a famous construction of mutually unbiased bases in prime dimensions that uses the eigenbases of cyclic subgroups of the Heisenberg-Weyl group. Less well-known perhaps is that orbits under the same group also form sets of mutually unbiased bases. Regarded as points in a Grassmannian space, we find that the individual bases from different sets of mutually unbiased bases lie at regular, repeating distances from one another and we conjecture an analytical expression for these distances based on their status as 2-designs.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2012. 359-364 p.
, AIP Conference Proceedings, ISSN 0094-243X ; 1508
Keyword [en]
Mutually unbiased bases, Heisenberg-Weyl group
National Category
Physical Sciences
URN: urn:nbn:se:su:diva-87986DOI: 10.1063/1.4773148OAI: diva2:608589
Quantum Theory: Reconsideration of Foundations 6
Available from: 2013-02-28 Created: 2013-02-28 Last updated: 2013-03-11Bibliographically approved
In thesis
1. Configurations in Quantum Information
Open this publication in new window or tab >>Configurations in Quantum Information
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Measurements play a central role in quantum information. This thesis looksat two types: contextual measurements and symmetric measurements. Contextualityoriginates from the Kochen-Specker theorem about hidden variablemodels and has recently undergone a subtle shift in its manifestation. Symmetricmeasurements are characterised by the regular polytopes they formin Bloch space (the vector space containing all density matrices) and are thesubject of several investigations into their existence in all dimensions.We often describe measurements by the vectors in Hilbert space ontowhich our operators project. In this sense, both contextual and symmetricmeasurements are connected to special sets of vectors. These vectors areoften special for another reason: they form congurations in a given incidencegeometry.In this thesis, we aim to show various connections between congurationsand measurements in quantum information. The congurations discussedhere would have been well-known to 19th and 20th century geometers andwe show they are relevant for advances in quantum theory today. Specically,the Hesse and Reye congurations provide proofs of measurement contextuality,both in its original form and its newer guise. The Hesse congurationalso ties together dierent types of symmetric measurements in dimension3called SICs and MUBswhile giving insights into the group theoreticalproperties of higher dimensional symmetric measurements.

Place, publisher, year, edition, pages
Department of Physics, Stockholm University, 2012. 47 p.
National Category
Other Physics Topics
Research subject
urn:nbn:se:su:diva-82921 (URN)
Available from: 2012-11-30 Created: 2012-11-30 Last updated: 2013-02-28Bibliographically approved

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Blanchfield, Kate
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