More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Joseph W. Iverson; John Jasper; Dustin G. Mixon

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arXiv · 2410.17379

More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$

Joseph W. Iverson·John Jasper·Dustin G. Mixon

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Abstract

We introduce a new infinite family of $d\times 2d$ equiangular tight frames. Many matrices in this family consist of two $d\times d$ circulant blocks. We conjecture that such equiangular tight frames exist for every $d$. We show that our conjecture holds for $d\leq 165$ by a computer-assisted application of a Newton-Kantorovich theorem. In addition, we supply numerical constructions that corroborate our conjecture for $d\leq 1500$.

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Joseph W. Iverson, John Jasper, Dustin G. Mixon. 2024-10-22. More on the optimal arrangement of $2d$ lines in $\mathbb{C}^d$. https://arxiv.org/abs/2410.17379

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