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
Aligned SICs and embedded tight frames in even dimensions
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 22019 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, no 42, article id 425302Article in journal (Refereed) Published
Abstract [en]

Alignment is a geometric relation between pairs of Weyl-Heisenberg SICs, one in dimension d and another in dimension d(d - 2), manifesting a well-founded conjecture about a number-theoretical connection between the SICs. In this paper, we prove that if d is even, the SIC in dimension d(d - 2) of an aligned pair can be partitioned into (d - 2)(2) tight d(2)-frames of rank d(d - 1)/2 and, alternatively, into d(2) tight (d - 2)(2) -frames of rank (d - 1) (d - 2)/2. The corresponding result for odd d is already known, but the proof for odd d relies on results which are not available for even d. We develop methods that allow us to overcome this issue. In addition, we provide a relatively detailed study of parity operators in the Clifford group, emphasizing differences in the theory of parity operators in even and odd dimensions and discussing consequences due to such differences. In a final section, we study implications of alignment for the symmetry of the SIC.

Place, publisher, year, edition, pages
2019. Vol. 52, no 42, article id 425302
Keywords [en]
SIC-POVM, frame theory, Weyl-Heisenberg group, symmetry, parity operator, Chinese remainder
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-175013DOI: 10.1088/1751-8121/ab434eISI: 000488015200001OAI: oai:DiVA.org:su-175013DiVA, id: diva2:1367337
Available from: 2019-11-03 Created: 2019-11-03 Last updated: 2019-11-03Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Search in DiVA

By author/editor
Andersson, OleDumitru, Irina
By organisation
Department of Physics
In the same journal
Journal of Physics A: Mathematical and Theoretical
Physical Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
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