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

TL;DR

This paper explores the construction of optimal subspace packings using symmetric and affine block designs and mutually unbiased bases, extending previous methods to generate a wide range of optimal Grassmannian designs and analyzing their properties.

Contribution

It generalizes existing construction techniques for optimal subspace packings, demonstrating their applicability to various block designs and establishing that optimal packings are fusion frames with optimal complements.

Findings

Extended construction methods to various block designs.

Proved all optimal packings are fusion frames.

Showed the orthoplex bound characterizes optimal packings.

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.