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

Kean Fallon; Joseph W. Iverson

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arXiv · 2312.09975

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

Kean Fallon·Joseph W. Iverson

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Abstract

We show the optimal coherence of $2d$ lines in $\mathbb{C}^{d}$ is given by the Welch bound whenever a skew Hadamard of order $d+1$ exists. Our proof uses a variant of Hadamard doubling that converts any equiangular tight frame of size $\tfrac{d-1}{2} \times d$ into another one of size $d \times 2d$. Among $d < 150$, this produces equiangular tight frames of new sizes when $d = 11$, $35$, $39$, $43$, $47$, $59$, $67$, $71$, $83$, $95$, $103$, $107$, $111$, $119$, $123$, $127$, $131$, and $143$.

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BibTeX RIS

Kean Fallon, Joseph W. Iverson. 2023-12-15. On the optimal arrangement of $2d$ lines in $\mathbb{C}^d$. https://arxiv.org/abs/2312.09975

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