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The Frame Potential, On Average
Stockholm University, Faculty of Science, Department of Physics. (KoF)
Stockholm University, Faculty of Science, Department of Mathematics.
2009 (English)In: Open systems & information dynamics, ISSN 1230-1612, Vol. 16, no 2-3, 145-156 p.Article in journal (Refereed) Published
Abstract [en]

A Symmetric Informationally Complete Positive Operator Valued Measure (SIC) consists of N-2 equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N-2 unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Weyl-Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytically compute the average of this function over Hilbert space. We also compute averages when the financial vector is placed in certain special subspaces defined by the Clifford group.

Place, publisher, year, edition, pages
2009. Vol. 16, no 2-3, 145-156 p.
URN: urn:nbn:se:su:diva-33787DOI: 10.1142/S1230161209000116ISI: 000269123700004OAI: diva2:283582
Available from: 2009-12-29 Created: 2009-12-29 Last updated: 2010-01-14Bibliographically approved

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Bengtsson, Ingemar
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