On the existence of equiangular tight frames

Author: klrg

August undefined, 2024

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. Web26 de fev. de 2024 · Abstract An equiangular tight frame (ETF) is an equal norm tight frame with the same sharp angles between the vectors. This work is an attempt to create a brief review with complete proofs and calculations of two directions of research on the equiangular tight frames (ETF): bounds of the spark of the ETF, namely the smallest …

Real Equiangular Frames - University of Missouri

Webconstruction of equiangular tight frames for ﬁnite dimensional real Hilbert spaces [21, 18, 8, 3, 10], relatively few means are known for constructing equiangular frames in the complex case (see, e.g. [11, 17, 7]). The problem of the existence of equiangular frames is known to be equivalent how many cups in 5 pounds flour

Tremain equiangular tight frames - ScienceDirect

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 … WebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical … Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be … how many cups in 5 litres of water

On the existence of equiangular tight frames - CORE

WebEquiangular Tight Frames Let {x m} be a collection of N unit vectors in Cd with N ≥ d A lower bound on the maximum correlation between a pair of vectors: max m6= n hx m, x ni ≥ s N −d d(N −1) def= µ(d,N) The bound is met if and only if 1. The vectors are equiangular 2. The vectors form a tight frame WebIt 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. high schools in georgetown scWeb26 de fev. de 2014 · The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in ... how many cups in 5 pounds of sugar

"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 ... " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

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 … Web1 de jul. de 2008 · Yet, despite their importance, we are far from having a complete understanding about the existence of equiangular tight frames. Some results can be found in [12,8,4,3,13,10,6,1,7,9,11]. A popular method to construct equiangular tight frames is based on conference matrices [8, 3,10].

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Web9 de abr. de 2024 · a so-called equiangular tight frame if and only if this lower. bound is saturated, meaning in particular that the subnor-malised projectors {d. n ... deciding the existence of EAMs (see e.g. [68 ... Webd2 and a pair of ETFs (equiangular tight frames) in dimensions d(d± 1)/2. We also show that a WH (Weyl Heisenberg covariant) SIC in odd dimension dis naturally associated to a pair of symmetric tight fusion frames in dimension d. We deduce two relaxations of the WH SIC existence problem. We also ﬁnd a reformulation of the problem in which ...

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 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.

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 … WebThe constructionoftheMercedes–Benz frame, thewell-known example of a tight frame on the plane, is generalized to the space Rn. The existence problems for the …

Web1 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 …

http://users.cms.caltech.edu/~jtropp/slides/Tro05-Complex-Equiangular-Talk.pdf how many cups in 5 ozWeb31 de mar. de 2024 · Title: Small projective codes and equiangular lines Abstract: How can one arrange \(d+k\) many vectors in \(\mathbb{R}^d\) so that they are as close to orthogonal as possible? Such arrangements are known as projective codes (or antipodal spherical codes) and are a natural generalization of balanced error-correcting codes. how many cups in 5 pounds of honeyWeb1 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 ... how many cups in 5 pounds of wheat berriesWeb14 de set. de 2015 · Abstract. An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a ... how many cups in 5.5 litersWeb4 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, … high schools in garrett county marylandWeb1 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 + … high schools in glasgow city councilWeb1 de abr. de 2015 · A table of these equiangular tight frames, as well as a review of many of the known constructions, may be found in [29]. As an example, one may always … how many cups in 50 ounces of water