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States that are far from being stabilizer states
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.ORCID iD: 0000-0002-4203-3180
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 42015 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 48, no 34, article id 345301Article in journal (Refereed) Published
Abstract [en]

Stabilizer states are eigenvectors of maximal commuting sets of operators in a finite Heisenberg group. States that are far from being stabilizer states include magic states in quantum computation, MUB-balanced states, and SIC vectors. In prime dimensions the latter two fall under the umbrella of minimum uncertainty states (MUSs) in the sense of Wootters and Sussman. We study the correlation between two ways in which the notion of ` far from being a stabilizer state' can be quantified. Two theorems valid for all prime dimensions are given, as well as detailed results for low dimensions. In dimension 7 we identify the MUB-balanced states as being antipodal to the SIC vectors within the set of MUS, in a sense that we make definite. In dimension 4 we show that the states that come closest to being MUS with respect to all of the six stabilizer MUBs are the fiducial vectors for Alltop MUBs.

Place, publisher, year, edition, pages
2015. Vol. 48, no 34, article id 345301
Keywords [en]
mutually unbiased bases, Heisenberg groups, Clifford group
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:su:diva-176195DOI: 10.1088/1751-8113/48/34/345301ISI: 000359668500010OAI: oai:DiVA.org:su-176195DiVA, id: diva2:1373589
Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved

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Andersson, DavidBengtsson, IngemarBlanchfield, Kate
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