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- W2951330406 abstract "A set of vectors of equal norm in $mathbb{C}^d$ represents equiangular lines if the magnitudes of the Hermitian inner product of every pair of distinct vectors in the set are equal. The maximum size of such a set is $d^2$, and it is conjectured that sets of this maximum size exist in $mathbb{C}^d$ for every $d geq 2$. We take a combinatorial approach to this conjecture, using mutually unbiased bases (MUBs) in the following 3 constructions of equiangular lines: (1) adapting a set of $d$ MUBs in $mathbb{C}^d$ to obtain $d^2$ equiangular lines in $mathbb{C}^d$, (2) using a set of $d$ MUBs in $mathbb{C}^d$ to build $(2d)^2$ equiangular lines in $mathbb{C}^{2d}$, (3) combining two copies of a set of $d$ MUBs in $mathbb{C}^d$ to build $(2d)^2$ equiangular lines in $mathbb{C}^{2d}$. For each construction, we give the dimensions $d$ for which we currently know that the construction produces a maximum-sized set of equiangular lines." @default.
- W2951330406 created "2019-06-27" @default.
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- W2951330406 date "2014-08-21" @default.
- W2951330406 modified "2023-09-27" @default.
- W2951330406 title "Constructions of complex equiangular lines from mutually unbiased bases" @default.
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