On the existence of equiangular tight frames

WebComplex Equiangular Tight Frames Joel A. Troppa aMathematics Department, The University of Michigan, 530 Church St., Ann Arbor, MI 48109-1043, USA ... First, one could demonstrate the existence of specific complex ETFs via constructive (or nonconstructive) means. Second, one could attempt to rule out the possibility that a complex http://users.cms.caltech.edu/~jtropp/slides/Tro05-Complex-Equiangular-Talk.pdf

Type of the equiangular tight frames with n+1 vectors in R^n

Webtight frame exists for each pair (d,N) with N ≤ 100 that meets the new conditions. The arguments also extend to deliver novel necessary conditions for the existence of … WebA Grassmannian frame is a collection of unit vectors which are optimally incoherent. The most accessible (and perhaps most beautiful) of Grassmannian frames are equiangular tight frames (ETFs); indeed, there are infinite families of known ETFs, whereas only finitely many non-ETF Grassmannianframesare knownto date. green monday headphones https://ambertownsendpresents.com

Complex Equiangular Tight Frames

Web25 de fev. de 2009 · A survey on equiangular tight frames in the space $$ \\mathbb{R}^n $$ is presented. Several equivalent definitions of a tight frame are given. The … Web4 de ago. de 2015 · Neither the existence of SIC-POVMs in higher-dimensional Hilbert spaces nor the nonexistence of MUBs in a six-dimensional Hilbert space has been proved. On the other hand, conditional SIC-POVMs are considered as equiangular tight frames. The existence of equiangular tight frames is also studied in many literature (e.g., [8, … Web1 de abr. de 2015 · Tables of the existence of equiangular tight frames. A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date, the vast … green monday online shop

(PDF) Resource-efficient high-dimensional entanglement …

Category:Real Equiangular Frames - University of Missouri

Tags:On the existence of equiangular tight frames

On the existence of equiangular tight frames

arXiv:1402.6429v1 [math.FA] 26 Feb 2014

Web17 de jul. de 2004 · Using a new one-to-one correspondence between equivalence classes of real equiangular tight frames and strongly regular graphs of a certain type, it has been veri ed that a real equiangular tight ... WebAbstract: An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and orthogonal rows of norm sqrt(N/d). Its key property is that the absolute inner …

On the existence of equiangular tight frames

Did you know?

Web1 de mar. de 2009 · The existence problems for the Mercedes–Benz systems and other more general equiangular tight frames are discussed. It is shown that the Welch inequality becomes the equality only on equiangular ... Web15 de out. de 2007 · We prove the existence of equiangular tight frames having n = 2 d-1 elements drawn from either C d or C d-1 whenever n is either 2 k-1 for k ∈ N, or a power …

Web3 Real equiangular tight frames In this section, we describe what is known about real equiangular tight frames. Throughout, we use ∃RETF(M,N) to denote the statement “there exists a real equiangular tight frame with parameters (M,N).” We start with some basic properties: Theorem 1 (see [39]). ∃RETF(M,N) implies each of the following: Webis an equiangular tight frame for R(M N). We call this the complementary equiangular tight frame. It follows that equiangular tight frames come in pairs and if M>2Nthen M<2(M N). So we only need to classify the equiangular tight frames for M>2N. Certain classes of equiangular tight frames always exist. Proposition 3.3: RN always has an 1.

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … Web6 de mar. de 2024 · We also develop a general framework of so-called harmonic BTFs and Steiner BTFs - which includes the equiangular cases, surprisingly, the development of …

Web6 de ago. de 2012 · An equiangular tight frame (ETF) is a d * n matrix that has orthogonal rows and unit-norm columns. ETFs have applications in communications, coding theory and quantum computing.

Web29 de set. de 2010 · Doubly transitive equiangular tight frames that contain regular simplices. M. Fickus, Evan C. Lake. Mathematics. ArXiv. 2024. An equiangular tight … green monday meaningWeb1 de out. de 2007 · Request PDF On the existence of equiangular tight frames An equiangular tight frame (ETF) is a d×N matrix that has unit-norm columns and … green monday holidayWeb1 de jan. de 2024 · For every V ≡ 1 or 3 mod 6 with V ≥ 3, there exists an equiangular tight frame of N vectors in C M with M = 1 6 ( V + 2) ( V + 3), N = 1 2 ( V + 1) ( V + 2). As illustrated by Tremain's original example above, this construction is real whenever the unimodular simplices come from real Hadamard matrices. In particular, a ( V + 1) × ( V + … green monday offersWeb开馆时间:周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 flying ship artWebIt is shown that the existence of frames and duals that attain the lower bound is related to the existence of equiangular tight frames (ETFs). Second, motivated by the scarcity of ETFs (which by default have dual ETFs), we examine the more general question of existence of equiangular frames that have equiangular duals. flying shiny sandwich recipeWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): An equiangular tight frame (ETF) is a d × N matrix that has unit-norm columns and … flying ship filderstadtWebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical … green monday piano keyboard girl