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math.FA2025
The impossibility of extending the Naimark complement
Emily J. King, Dustin G. Mixon
We show that there is no extension of the Naimark complement to arbitrary frames that satisfies three fundamental properties of the Naimark complement of Parseval frames.
math.FA2025
Nearly tight weighted 2-designs in complex projective spaces of every dimension
John Jasper, Dustin G. Mixon
We use dense Sidon sets to construct small weighted projective 2-designs. This represents quantitative progress on Zauner's conjecture.