Zobrazeno 1 - 10
of 227
pro vyhledávání: '"HAAS, JOHN A."'
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 un
Externí odkaz:
http://arxiv.org/abs/1806.03549
We will review the major results in finite dimensional real phase retrieval for vectors and projections. We then (1)prove that many of these theorems hold in infinite dimensions, (2) give counter-examples to show that many others fail in infinite dim
Externí odkaz:
http://arxiv.org/abs/1804.01139
Autor:
Bodmann, Bernhard, Haas, John
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief introduction, we disc
Externí odkaz:
http://arxiv.org/abs/1709.01958
Autor:
Botelho-Andrade, Sara, Casazza, Peter G., Cheng, Desai, Haas, John, Tran, Tin T., Tremain, Janet C., Xu, Zhiqiang
We show that a scalable frame does phase retrieval if and only if the hyperplanes of its orthogonal complements do phase retrieval. We then show this result fails in general by giving an example of a frame for $\mathbb R^3$ which does phase retrieval
Externí odkaz:
http://arxiv.org/abs/1703.02678
We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular Tight Frame
Externí odkaz:
http://arxiv.org/abs/1703.01786
Equiangular tight frames (ETFs) and biangular tight frames (BTFs) - sets of unit vectors with basis-like properties whose pairwise absolute inner products admit exactly one or two values, respectively - are useful for many applications. A well-unders
Externí odkaz:
http://arxiv.org/abs/1610.03142
Autor:
Bodmann, Bernhard G., Haas, John I.
The construction of optimal line packings in real or complex Euclidean spaces has shown to be a tantalizingly difficult task, because it includes the problem of finding maximal sets of equiangular lines. In the regime where equiangular lines are not
Externí odkaz:
http://arxiv.org/abs/1607.04546
Autor:
Casazza, Peter G., Haas, John I.
We study the rigidity properties of Grassmannian frames: basis-like sets of unit vectors that correspond to optimal Grassmannian line packings. It is known that Grassmannian frames characterized by the Welch bound must satisfy the restrictive geometr
Externí odkaz:
http://arxiv.org/abs/1605.02012
Autor:
Bodmann, Bernhard G., Haas, John
Equiangular tight frames are examples of Grassmannian line packings for a Hilbert space. More specifically, according to a bound by Welch, they are minimizers for the maximal magnitude occurring among the inner products of all pairs of vectors in a u
Externí odkaz:
http://arxiv.org/abs/1509.05333
Autor:
Bodmann, Bernhard G., Haas, John
This paper concerns the geometric structure of optimizers for frame potentials. We consider finite, real or complex frames and rotation or unitarily invariant potentials, and mostly specialize to Parseval frames, meaning the frame potential to be opt
Externí odkaz:
http://arxiv.org/abs/1407.1663