Algebraic units, anti-unitary symmetries, and a small catalogue of SICs
| Autor: | Ingemar Bengtsson |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Quantum Physics
Nuclear and High Energy Physics Pure mathematics Mathematics - Number Theory Dimension (graph theory) FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Algebraic number field Theoretical Computer Science Computational Theory and Mathematics Simple (abstract algebra) Norm (mathematics) Homogeneous space FOS: Mathematics Number Theory (math.NT) Algebraic number Equiangular lines Quantum Physics (quant-ph) Mathematical Physics Mathematics Fundamental unit (number theory) |
| Zdroj: | Quantum Information and Computation. 20:400-417 |
| ISSN: | 1533-7146 |
| Popis: | In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form $n^2+3$ the base field has a fundamental unit of negative norm, and there exists a SIC with anti-unitary symmetry. We give eight examples of exact solutions of this kind, for which we have endeavoured to make them as simple as we can---as a belated reply to the referee of an earlier publication, who claimed that our exact solution in dimension 28 was too complicated to be fit to print. An interesting feature of the simplified solutions is that the components of the fiducial vectors largely consist of algebraic units. 18 pages, 2 figures; minor corrections in version 2 |
| Databáze: | OpenAIRE |
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