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HRT counterexamples with exponential tails
John Jasper, Dustin G. Mixon
We build on the recent breakthrough of Faulhuber, Petersen, van Velthoven, and Voigtlaender that disproved the HRT conjecture with a Schwartz function and a -point configuratio…
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…
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.
Diagonals of self-adjoint operators II: Non-compact operators
Marcin Bownik, John Jasper
Given a self-adjoint operator on a separable infinite-dimensional Hilbert space we study the problem of characterizing the set of all possible diagonals of .…
Equiangular tight frames from group divisible designs
Matthew Fickus, John Jasper
An equiangular tight frame (ETF) is a type of optimal packing of lines in a real or complex Hilbert space. In the complex case, the existence of an ETF of a given size remains an o…
Equiangular tight frames that contain regular simplices
Matthew Fickus, John Jasper, Emily J. King +1
An equiangular tight frame (ETF) is a type of optimal packing of lines in Euclidean space. A regular simplex is a special type of ETF in which the number of vectors is one more tha…