Dimension towers of SICs. II. Some constructions
- URL: http://arxiv.org/abs/2202.00600v1
- Date: Tue, 1 Feb 2022 17:44:01 GMT
- Title: Dimension towers of SICs. II. Some constructions
- Authors: Ingemar Bengtsson and Basudha Srivastava
- Abstract summary: A SIC is a maximal equiangular tight frame in a finite dimensional Hilbert space.
We provide a recipe for how to calculate sets of vectors in dimension $d(d-2)$ that share these properties.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A SIC is a maximal equiangular tight frame in a finite dimensional Hilbert
space. Given a SIC in dimension $d$, there is good evidence that there always
exists an aligned SIC in dimension $d(d-2)$, having predictable symmetries and
smaller equiangular tight frames embedded in them. We provide a recipe for how
to calculate sets of vectors in dimension $d(d-2)$ that share these properties.
They consist of maximally entangled vectors in certain subspaces defined by the
numbers entering the $d$ dimensional SIC. However, the construction contains
free parameters and we have not proven that they can always be chosen so that
one of these sets of vectors is a SIC. We give some worked examples that, we
hope, may suggest to the reader how our construction can be improved. For
simplicity we restrict ourselves to the case of odd dimensions.
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