7 papers · 1 filter
The Singer-Zauner gap for equiangular tight frames
Matthew Fickus, John Jasper, Dustin G. Mixon
We show that there does not exist a complex equiangular tight frame with \[ d^2-d+1<n<d^2. \] The proof, which originated from an internal model at OpenAI, mimics the r…
Approximation theorems in bilipschitz invariant theory
Jameson Cahill, Joseph W. Iverson, Dustin G. Mixon +1
Bilipschitz invariant theory concerns low-distortion embeddings of orbit spaces into Euclidean space. To date, embeddings with the smallest-possible distortion are known for only a…
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.
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.
Injectivity, stability, and positive definiteness of max filtering
Dustin G. Mixon, Yousef Qaddura
Given a real inner product space V and a group G of linear isometries, max filtering offers a rich class of G-invariant maps. In this paper, we identify nearly sharp conditions und…
A lower bound for the Balan--Jiang matrix problem
Afonso S. Bandeira, Dustin G. Mixon, Stefan Steinerberger
We prove the existence of a positive semidefinite matrix such that any decomposition into rank-1 matrices has to have factors with a large …