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This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC).
R. W. H. T. Hudson 1905 Kummer’s Quartic Surface
1905
Earlier work this paper cites.
C. C. Grove 1906 The syzygetic pencil of cubics with a new geometrical development of its Hesse Group, G 216 G_{216}
1906
Earlier work this paper cites.
F. Klein 1926 Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert
1926
Earlier work this paper cites.
H. Weyl 1932 Theory of Groups and Quantum Mechanics
1932
Earlier work this paper cites.
A. S. Eddington 1935 New Pathways in Science
1935
Earlier work this paper cites.
A. F. Horadam 1957, A locus in [8] invariant under a group of order 51840 × \times 81, Quart. J. Math. Oxford
1957
Earlier work this paper cites.
I. D. Ivanović 1981, Geometrical description of quantal state determination, J. Phys
1981
Earlier work this paper cites.
S. T. Flammia, A. Silberfarb, and C. M. Caves 2005, Minimal informationally complete measurements for pure states, Found. Phys
1985
Earlier work this paper cites.
K. Hulek 1986, Projective geometry of elliptic curves, Asterisque
1986
Earlier work this paper cites.
W. K. Wootters 1987, A Wigner-function formulation of finite-state quantum mechanics, Ann. Phys
1987
Earlier work this paper cites.
W. K. Wootters and B. D. Fields 1989, Optimal state-determination by mutually unbiased measurements, Ann. Phys
1989
Earlier work this paper cites.
D. I. Fivel 1995, Remarkable phase oscillations appearing in the lattice dynamics of Einstein-Podolsky-Rosen states, Phys. Rev. Lett
1995
Cited alongside, same era.
D. Gottesman 1998, A theory of fault-tolerant quantum computation, Phys. Rev
1998
Cited alongside, same era.
C. G. Gibson 1998 Elementary Geometry of Algebraic Curves
1998
Cited alongside, same era.
G. Zauner 1999 Quantendesigns. Grundzüge einer nichtkommutativen Designtheorie
1999
Cited alongside, same era.
D. C. Brody and L. P. Hughston 2001, Geometric quantum mechanics, J. Geom. Phys. 38
2001
Cited alongside, same era.
S. Bandyopadhayay, P. O. Boykin, V. Roychowdhury, and F. Vatan 2002, A new proof for the existence of a mutually unbiased bases, Algorithmica
W. Tadej and K. Życzkowski 2006, A concise guide to complex Hadamard matrices, Open Syst. Inf. Dyn. 13
2006
Later among the works it cites.
L. P. Hughston 2007, seminar at the Perimeter Institute
2007
Later among the works it cites.
2007
Later among the works it cites.
M. Khatirinejad 2008, On Weyl-Heisenberg orbits of equiangular lines, J. Algebr. Comb. 28
2008
Later among the works it cites.
A. Belovs 2008, Welch Bounds and Quantum State Tomography
2008
Later among the works it cites.
A. J. Scott and M. Grassl 2009, SIC-POVMs: A new computer study, eprint: arXiv:0910.5784
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2002
Cited alongside, same era.
J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves 2004, Symmetric informationally complete quantum measurements, J. Math. Phys
2004
Cited alongside, same era.
I. Dolgachev 2004, Abstract configurations in algebraic geometry, in Proc. of the Fano Conference
2004
Cited alongside, same era.
D. M. Appleby 2005, SIC-POVMs and the extended Clifford group, J. Math. Phys
2005
Cited alongside, same era.
D. Gross, Hudson’s theorem for finite dimensional quantum systems, J. Math. Phys
2006
Cited alongside, same era.
O. Hesse 1844, Über die Wendepuncte der Curven dritter Ordnung, J. Reine Angew. Math
Cited in the paper.
J. Plücker 1835 System der analytischen Geometrie, auf neue Betrachtungsweisen gegründet
Cited in the paper.
2009
Later among the works it cites.
D. M. Appleby 2009, SIC-POVMs and MUBs: Geometrical relationships in prime dimensions, in L. Accardi et al (eds.) Proc of the Växjö Conference on Foundations of Probability and Physics - 5
2009
Later among the works it cites.
C. Godsil and A. Roy 2009, Equiangular lines, mutually unbiased bases, and spin models, Euro. J. Combin
2009
Later among the works it cites.
I. Bengtsson and Å. Ericsson 2009 unpublished
2009
Later among the works it cites.