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Equiangular tight frames (ETFs) may be used to construct examples of feasiblepoints for semidefinite programs arising in sum-of-squares (SOS) optimization.We show how generalizing the calculations in a recent work of the authors' thatexplored this connection also yields new bounds on the sparsity of (both realand complex) ETFs. One corollary shows that Steiner ETFs corresponding tofinite projective planes are optimally sparse in the sense of achievingtightness in a matrix inequality controlling overlaps between sparsity patternsof distinct rows of the synthesis matrix. We also formulate several naturalopen problems concerning further generalizations of our technique.

Sum-of-Squares Optimization and the Sparsity Structure of Equiangular Tight Frames