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arXiv · 1806.03549

Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases

Peter G. Casazza·John I. Haas·Joshua Stueck·Tin T. Tran
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Abstract

We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the authors use maximal affine block designs and maximal sets of mutually unbiased bases to construct Grassmannian $2$-designs, we show that their method extends to other types of block designs, leading to a plethora of optimal subspace packings characterized by the orthoplex bound. More generally, we show that any optimal chordal packing is necessarily a fusion frame and that its spatial complement is also optimal.

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Peter G. Casazza, John I. Haas, Joshua Stueck, Tin T. Tran. 2018-06-09. Constructions and properties of optimally spread subspace packings via symmetric and affine block designs and mutually unbiased bases. https://arxiv.org/abs/1806.03549

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