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We present a conjectured family of SIC-POVMs which have an additional symmetry group whose size is growing with the dimension.
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J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, “Symmetric informationally complete quantum measurements,” Journal of Mathematical Physics 45
2004
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D. M. Appleby, “Symmetric informationally complete-positive operator valued measures and the extended Clifford group,” Journal of Mathematical Physics 46
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M. Grassl, “Tomography of quantum states in small dimensions,” Electronic Notes in Discrete Mathematics 20
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A. J. Scott and M. Grassl, “Symmetric informationally complete positive-operator-valued measures: A new computer study,” Journal of Mathematical Physics 51
2010
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N. J. A. Sloane (editor), “The on-line encyclopedia of integer sequences,” published electronically at https://oeis.org (2010)
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G. Zauner, “Quantum designs: Foundations of a non-commutative design theory,” International Journal of Quantum Information 9
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C. A. Fuchs, M. C. Hoang, and B. C. Stacey, “The SIC question: History and state of play,” axioms 6
2017
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M. Grassl and S. Waldron, “Computing projective symmetries of frames,” (2017), in preparation
2017
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http://sicpovm.markus-grassl.de, (2017)
2017
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2017
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M. Grassl, A. J. Scott, and U. Seyfarth, “Symmetries of Weyl-Heisenberg SIC-POVMs,” (2017), in preparation
2017
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2016
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A. J. Scott, “SICs: extending the list of solutions,” arXiv:1703.03993 [quant-ph] (2017)
2017
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Cited in the paper.