FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3099338996> ?p ?o ?g. }

• W3099338996 endingPage "3475" @default.
• W3099338996 startingPage "3449" @default.
• W3099338996 abstract "Five years ago, Lane Hughston showed that some of the symmetric informationally complete positive operator valued measures (SICs) in dimension 3 coincide with the Hesse configuration (a structure well known to algebraic geometers, which arises from the torsion points of a certain elliptic curve). This connection with elliptic curves is signalled by the presence of linear dependencies among the SIC vectors. Here we look for analogous connections between SICs and algebraic geometry by performing computer searches for linear dependencies in higher dimensional SICs. We prove that linear dependencies will always emerge in Weyl-Heisenberg orbits when the fiducial vector lies in a certain subspace of an order 3 unitary matrix. This includes SICs when the dimension is divisible by 3 or equal to 8 mod 9. We examine the linear dependencies in dimension 6 in detail and show that smaller dimensional SICs are contained within this structure, potentially impacting the SIC existence problem. We extend our results to look for linear dependencies in orbits when the fiducial vector lies in an eigenspace of other elements of the Clifford group that are not order 3. Finally, we align our work with recent studies on representations of the Clifford group." @default.
• W3099338996 created "2020-11-23" @default.
• W3099338996 creator A5015798097 @default.
• W3099338996 creator A5058674988 @default.
• W3099338996 creator A5063266138 @default.
• W3099338996 creator A5090875555 @default.
• W3099338996 date "2013-07-14" @default.
• W3099338996 modified "2023-09-23" @default.
• W3099338996 title "Linear dependencies in Weyl–Heisenberg orbits" @default.
• W3099338996 cites W1599714836 @default.
• W3099338996 cites W1977809994 @default.
• W3099338996 cites W1981733373 @default.
• W3099338996 cites W1987245344 @default.
• W3099338996 cites W1987576785 @default.
• W3099338996 cites W2003796340 @default.
• W3099338996 cites W2010339566 @default.
• W3099338996 cites W2015049075 @default.
• W3099338996 cites W2021578093 @default.
• W3099338996 cites W2058558225 @default.
• W3099338996 cites W2086848886 @default.
• W3099338996 cites W2094366212 @default.
• W3099338996 cites W2140122025 @default.
• W3099338996 cites W2166655634 @default.
• W3099338996 cites W2963646190 @default.
• W3099338996 cites W3099753513 @default.
• W3099338996 cites W3101740473 @default.
• W3099338996 cites W3103349989 @default.
• W3099338996 cites W3106019570 @default.
• W3099338996 cites W4230623248 @default.
• W3099338996 doi "https://doi.org/10.1007/s11128-013-0609-6" @default.
• W3099338996 hasPublicationYear "2013" @default.
• W3099338996 type Work @default.
• W3099338996 sameAs 3099338996 @default.
• W3099338996 citedByCount "22" @default.
• W3099338996 countsByYear W30993389962014 @default.
• W3099338996 countsByYear W30993389962015 @default.
• W3099338996 countsByYear W30993389962016 @default.
• W3099338996 countsByYear W30993389962017 @default.
• W3099338996 countsByYear W30993389962018 @default.
• W3099338996 countsByYear W30993389962019 @default.
• W3099338996 countsByYear W30993389962020 @default.
• W3099338996 countsByYear W30993389962021 @default.
• W3099338996 countsByYear W30993389962022 @default.
• W3099338996 countsByYear W30993389962023 @default.
• W3099338996 crossrefType "journal-article" @default.
• W3099338996 hasAuthorship W3099338996A5015798097 @default.
• W3099338996 hasAuthorship W3099338996A5058674988 @default.
• W3099338996 hasAuthorship W3099338996A5063266138 @default.
• W3099338996 hasAuthorship W3099338996A5090875555 @default.
• W3099338996 hasBestOaLocation W30993389962 @default.
• W3099338996 hasConcept C100856211 @default.
• W3099338996 hasConcept C106487976 @default.
• W3099338996 hasConcept C121332964 @default.
• W3099338996 hasConcept C13336665 @default.
• W3099338996 hasConcept C134306372 @default.
• W3099338996 hasConcept C136119220 @default.
• W3099338996 hasConcept C158693339 @default.
• W3099338996 hasConcept C159985019 @default.
• W3099338996 hasConcept C17744445 @default.
• W3099338996 hasConcept C192562407 @default.
• W3099338996 hasConcept C199539241 @default.
• W3099338996 hasConcept C202444582 @default.
• W3099338996 hasConcept C32834561 @default.
• W3099338996 hasConcept C33676613 @default.
• W3099338996 hasConcept C33923547 @default.
• W3099338996 hasConcept C49766605 @default.
• W3099338996 hasConcept C62520636 @default.
• W3099338996 hasConcept C67820243 @default.
• W3099338996 hasConcept C9376300 @default.
• W3099338996 hasConceptScore W3099338996C100856211 @default.
• W3099338996 hasConceptScore W3099338996C106487976 @default.
• W3099338996 hasConceptScore W3099338996C121332964 @default.
• W3099338996 hasConceptScore W3099338996C13336665 @default.
• W3099338996 hasConceptScore W3099338996C134306372 @default.
• W3099338996 hasConceptScore W3099338996C136119220 @default.
• W3099338996 hasConceptScore W3099338996C158693339 @default.
• W3099338996 hasConceptScore W3099338996C159985019 @default.
• W3099338996 hasConceptScore W3099338996C17744445 @default.
• W3099338996 hasConceptScore W3099338996C192562407 @default.
• W3099338996 hasConceptScore W3099338996C199539241 @default.
• W3099338996 hasConceptScore W3099338996C202444582 @default.
• W3099338996 hasConceptScore W3099338996C32834561 @default.
• W3099338996 hasConceptScore W3099338996C33676613 @default.
• W3099338996 hasConceptScore W3099338996C33923547 @default.
• W3099338996 hasConceptScore W3099338996C49766605 @default.
• W3099338996 hasConceptScore W3099338996C62520636 @default.
• W3099338996 hasConceptScore W3099338996C67820243 @default.
• W3099338996 hasConceptScore W3099338996C9376300 @default.
• W3099338996 hasIssue "11" @default.
• W3099338996 hasLocation W30993389961 @default.
• W3099338996 hasLocation W30993389962 @default.
• W3099338996 hasLocation W30993389963 @default.
• W3099338996 hasLocation W30993389964 @default.
• W3099338996 hasOpenAccess W3099338996 @default.
• W3099338996 hasPrimaryLocation W30993389961 @default.
• W3099338996 hasRelatedWork W1495674077 @default.
• W3099338996 hasRelatedWork W2127273444 @default.
• W3099338996 hasRelatedWork W2239199320 @default.

• next