Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Dimension towers of SICs. I. Aligned SICs and embedded tight frames
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: 42017 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 11, article id 112201Article in journal (Refereed) Published
Abstract [en]

Algebraic number theory relates SIC-POVMsin dimension d > 3 to those in dimension d(d - 2). We define a SIC in dimension d(d - 2) to be aligned to a SIC in dimension d if and only if the squares of the overlap phases in dimension d appear as a subset of the overlap phases in dimension d(d - 2) in a specifiedway. We give 19 (mostly numerical) examples of aligned SICs. We conjecture that given any SIC in dimension d, there exists an aligned SIC in dimension d(d - 2). In all our examples, the aligned SIC has lower dimensional equiangular tight frames embedded in it. If d is odd so that a natural tensor product structure exists, we prove that the individual vectors in the aligned SIC have a very special entanglement structure, and the existence of the embedded tight frames follows as a theorem. If d - 2 is an odd prime number, we prove that a complete set of mutually unbiased bases can be obtained by reducing an aligned SIC to this dimension.

Place, publisher, year, edition, pages
2017. Vol. 58, no 11, article id 112201
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-180145DOI: 10.1063/1.4999844ISI: 000416831900018OAI: oai:DiVA.org:su-180145DiVA, id: diva2:1416786
Available from: 2020-03-25 Created: 2020-03-25 Last updated: 2020-03-25Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Bengtsson, IngemarDumitru, Irina
By organisation
Department of Physics
In the same journal
Journal of Mathematical Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf