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

2018/06/09 by Casazza, Peter G., Haas, John I., Stueck, Joshua +1
#42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1806.03549

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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