Fetching the paper…
Reading the bibliography…
We show that naturally associated to a SIC (symmetric informationally complete positive operator valued measure or SIC-POVM) in dimension d there are a number of higher dimensional structures: specifically a projector and a complex Hadamard matrix in dimension d squared and a pair of ETFs (equiangular tight frames) in dimensions d(d-1)/2, d(d+1)/2.
E. J. King, Creating subspace packings from other subspace packings, arXiv:1902.07145
1902
Earlier work this paper cites.
M. A. Neumark, On a representation of additive operator set functions, C. R. (Doklady) Acad. Sci. URSS (N.S.) 41
1943
Earlier work this paper cites.
J. Schwinger, Unitary operator bases
1960
Earlier work this paper cites.
F. Szöllősi, Complex Hadamard matrices and equiangular tight frames
1962
Earlier work this paper cites.
L. R. Welch, Lower bounds on the maximum cross correlation of signals
1974
Earlier work this paper cites.
S. G. Hoggar, 64 lines from a quaternionic polytope, Geometriae Dedicata 69
1998
Earlier work this paper cites.
D. Han and D. R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc. 147
2000
Earlier work this paper cites.
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, Symmetric informationally complete quantum measurements
2004
Earlier work this paper cites.
P. G. Casazza and G. Kutyniok, Frames of subspaces , Contemporary Mathematics 345
2004
Earlier work this paper cites.
R. B. Holmes and V. I. Paulsen, Optimal frames for erasures
2004
Earlier work this paper cites.
D. M. Appleby, SIC-POVMs and the extended Clifford group
2005
Earlier work this paper cites.
A. Klappenecker and M. Rötteler, Mutually unbiased bases are projective 2-designs
2005
Earlier work this paper cites.
W. Tadej and K. Życzkowski, A concise guide to complex Hadamard matrices
2006
Earlier work this paper cites.
D. M. Appleby, Symmetric informationally complete measurements of arbitrary rank, Opt. Spect. 103
2007
Cited alongside, same era.
M.A. Sustik, J.A. Tropp, I.S. Dhillon, R.W. Heath Jr., On the existence of equiangular tight frames , Linear Algebra Appl. 426
2007
Cited alongside, same era.
A. Belovs, Welch bounds and quantum state tomography
2008
Cited alongside, same era.
G. Kutyniok, A. Pezeshki, R. Calderbank, and T. Liu, Robust dimension reduction, fusion frames, and Grassmannian packings, Appl. Comput. Harmon. Anal. 26
2009
Cited alongside, same era.
A. J. Scott and M. Grassl, SIC-POVMs: A new computer study
2010
Cited alongside, same era.
B. G. Bodmann and H. J. Elwood, Complex equiangular Parsival frames and Seidel matrices containing pth roots of unity
D. M. Appleby, H. Yadsan-Appleby, and G. Zauner, Galois automorphisms of symmetric measurements
2013
Later among the works it cites.
M. A. Graydon and D. M. Appleby, Quantum conical designs, J. Phys. A 49
2016
Later among the works it cites.
B. R. Karlsson, BCCB complex Hadamard matrices of order 9, and MUBs
2016
Later among the works it cites.
C. A. Fuchs, M. C. Hoan, and B. C. Stacey, The SIC question: History and state of play
2017
Later among the works it cites.
M. Grassl and A. J. Scott, Fibonacci-Lucas SIC-POVMs , J. Math. Phys. 58
2017
Later among the works it cites.
G. S. Kopp, Indefinite theta functions and zeta functions , PhD Thesis, The University of Michigan, 2017
2017
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2010
Cited alongside, same era.
G. Zauner: Quantendesigns. Grundzüge einer nichtkommutativen Designtheorie
2011
Cited alongside, same era.
P. G. Casazza, M. Fickus, D. G. Mixon, Y. Wang, and Z. Zhou, Constructing tight fusion frames , Applied and Computational Harmonic Analysis 30
2011
Cited alongside, same era.
D. M. Appleby, S. T. Flammia, and C. A. Fuchs, The Lie algebraic significance of symmetric informationally complete measurements, J. Math. Phys. 52
2011
Cited alongside, same era.
2011
Cited alongside, same era.
M. Fickus, D.G. Mixon, J.C. Tremain, Constructing a large family of equiangular tight frames
2011
Cited alongside, same era.
S. Datta, S. Howard, D. Cochran, Geometry of the Welch Bounds, Linear Algebra Appl. 437
2012
Cited alongside, same era.
M. Appleby, I. Bengtsson, I. Dumitru and S. Flammia, Dimension Towers of SICs. I. Aligned SICs and embedded tight frames , J. Math. Phys. 58
2017
Later among the works it cites.
S. Waldron, A sharpening of the Welch bounds and the existence of real and complex spherical t t -designs , IEEE Trans. Inf. Theory 63
2017
Later among the works it cites.
W. Bruzda, D. Goyeneche, K. Życzkowski, Quantum measurements with prescribed symmetry , Phys. Rev. A 96
2017
Later among the works it cites.
M. Fickus, J. Jasper, D.. G. Mixon, and C. E. Watson, A brief introduction to equi-chordal and equi-isoclinic tight fusion frames, Wavelets and Sparsity XVII (Y. M. Lu, D. Van De Ville, and M. Papadakis, eds.), Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10394, 2017
2017
Later among the works it cites.
D. Goyeneche and O. Turek, Equiangular tight frames and unistochastic matrices
2017
Later among the works it cites.
M. Appleby, T.-Y. Chien, S. Flammia, and S. Waldron, Constructing exact symmetric informationally complete measurements from numerical solutions
2018
Later among the works it cites.
M. Fickus, J. Jasper, D. G. Mixon, J. Peterson, Tremain equiangular tight frames
2018
Later among the works it cites.