On the existence of equiangular tight frames

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Web22 de out. de 2014 · In a recent paper, Holmes and Paulsen established a necessary condition for the existence of an N-vector equiangular tight frame in a d-dimensional … 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 …

TIGHT FRAMES, HADAMARD MATRICES AND ZAUNER’S CONJECTURE

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 of a prime such that n ≡ 3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2 d-element equiangular tight frame based on ... 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 order by where顺序

Equiangular tight frames with centroidal symmetry

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 … WebFinally, we mention a general necessary condition for the existence of equiangular tight frames. Compared to the local conditions described above, it is a global condition depending on solely the parameters n and m. Theorem 2.5 (Naimark, see e.g. [7]). 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 … irc newborn baby kit

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Real Equiangular Frames - University of Missouri

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 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 tight frames (if ... 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 ... irc network statsWebIt 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. irc network split

"Web31 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. " - On the existence of equiangular tight frames

On the existence of equiangular tight frames

$arXiv:0805.2014v2 [math.FA] 1 Sep 2008$

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. 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 ...

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WebAn equiangular tight frame (ETF) is a d ×N matrix that has unit-norm columns and orthogonal rows of norm √ … 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 …

Web1 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 … 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

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 … 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

WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda):

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 … irc nf20Web1 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]. irc networks channelsWeb(equiangular lines, tight frame, ETF) may be expressed using only polynomials and an order-2 ﬁeld automorphism (complex conjugation). From this light, our 1Elsewhere in the literature, “Zauner’s conjecture” may refer either to Conjecture 1.1 or to one of several stronger statements that posit the existence of equiangular lines with ... irc nf67Webtight 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 equiangular tight frames whose Gram matrices have entries drawn from a discrete set of complex numbers. Index Terms—tight frame, equiangular lines, optimal Grassman- irc nf27Web4 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, … irc network hosting serviceWebSequences, or optimal Grassmannian frames, or two-uniform frames. We prefer the more descriptive term “equiangular tight frame.” 1.1 Summary of Results The numerical evidence suggests that ETFs do not arise for most pairs (d,N). See [21, Sec. V-C] for details of this investigation. The goal of the present paper irc new jerseyWebThe Internet Archive offers over 20,000,000 freely downloadable books and texts. There is also a collection of 2.3 million modern eBooks that may be borrowed by anyone with a free archive.org account. Borrow a Book Books on Internet Archive are … irc networking