Surveying points in the complex projective plane

Fields Institute, Ontario, the Perimeter Insti-tute, Ontario, and Tulane University, New Orleans, S.Abramsky, D.Appleby, R.Blume-Kohout, D.Brody, H.Brown, S.Flammia, C.Fuchs, L.Hardy, and H.Zhu for stimulating discussions. SMS acknowledges support arising from visits to the University of Nijmegen, the University of Sofia and the University of Turin, and thanks N.Lora Lamia for helpful comments. J.Armstrong.

[1]  Markus Grassl,et al.  Computing Equiangular Lines in Complex Space , 2008, MMICS.

[2]  Steven T. Flammia.  On SIC-POVMs in prime dimensions , 2006 .

[3]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[4]  Bernd Sturmfels.  What is a groebner basis , 2005 .

[5]  A. J. Scott,et al.  SIC-POVMs: A new computer study , 2009 .

[6]  K. Nomizu,et al.  Foundations of Differential Geometry , 1963 .

[7]  M. Sentís.  Quantum theory of open systems , 2002 .

[8]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[9]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[10]  Christopher A. Fuchs,et al.  Group theoretic, lie algebraic and Jordan algebraic formulations of the sic existence problem , 2013, Quantum Inf. Comput..

[11]  S. Sternberg,et al.  Symplectic Techniques in Physics , 1984 .

[12]  H. Weyl.  The Theory Of Groups And Quantum Mechanics , 1931 .

[13]  Joseph M. Renes,et al.  Symmetric informationally complete quantum measurements , 2003, quant-ph/0310075.

[14]  W. Thurston,et al.  Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.

[15]  Huangjun Zhu.  SIC POVMs and Clifford groups in prime dimensions , 2010, 1003.3591.

[16]  Abhay Ashtekar,et al.  Geometrical Formulation of Quantum Mechanics , 1999 .

[17]  A. J. Scott,et al.  Symmetric informationally complete positive-operator-valued measures: A new computer study , 2010 .

[18]  Akihiro Munemasa,et al.  Equiangular lines in Euclidean spaces , 2014, J. Comb. Theory, Ser. A.

[19]  W. Wootters.  Quantum Measurements and Finite Geometry , 2004, quant-ph/0406032.

[20]  Thomas Durt,et al.  About mutually unbiased bases in even and odd prime power dimensions , 2005 .

[21]  T. Kibble.  Geometrization of quantum mechanics , 1979 .

[22]  S. Salamon,et al.  Twistor lines on cubic surfaces , 2012, 1212.2851.

[23]  S. G. Hoggar.  64 Lines from a Quaternionic Polytope , 1998 .

[24]  Ferenc Szöllősi,et al.  All complex equiangular tight frames in dimension 3 , 2014 .

[25]  G. B. Mathews,et al.  Kummer's Quartic Surface , 1990 .

[26]  Ferenc SzollHosi,et al.  All complex equiangular tight frames in dimension 3 , 2014, 1402.6429.

[27]  L. Ballentine,et al.  Probabilistic and Statistical Aspects of Quantum Theory , 1982 .

[28]  G. Mihaylov.  Toric moment mappings and Riemannian structures , 2008, 0810.2799.

[29]  David Marcus Appleby,et al.  Galois automorphisms of a symmetric measurement , 2012, Quantum Inf. Comput..

[30]  D. M. Appleby.  Symmetric informationally complete–positive operator valued measures and the extended Clifford group , 2005 .

[31]  David Marcus Appleby,et al.  Linear dependencies in Weyl–Heisenberg orbits , 2013, Quantum Inf. Process..

[32]  E. Wigner.  Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren , 1931 .

[33]  W. Thurston,et al.  Three-Dimensional Geometry and Topology, Volume 1 , 1997, The Mathematical Gazette.

[34]  G. Gibbons.  Typical states and density matrices , 1992 .

[35]  Amir Kalev,et al.  Construction of all general symmetric informationally complete measurements , 2013, 1305.6545.

[36]  Aharonov,et al.  Geometry of quantum evolution. , 1990, Physical review letters.

[37]  D. Mumford,et al.  A rank 2 vector bundle on P4 with 15,000 symmetries , 1973 .

[38]  E. Guth,et al.  Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren , 1932 .

[39]  Hsien-Chtjng Wang,et al.  TWO-POINT HOMOGENEOUS SPACES , 1952 .

[40]  G. Zauner,et al.  QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY , 2011 .

[41]  L. Hughston,et al.  Geometry of stochastic state vector reduction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[42]  D. Brody,et al.  Geometric quantum mechanics , 1999, quant-ph/9906086.

[43]  D. M. Appleby.  SIC-POVMs and the Extended Clifford Group , 2004 .

[44]  On Wigner's theorem , 2011, 1112.2133.

[45]  Stefan Steidel,et al.  Gröbner bases of symmetric ideals , 2012, J. Symb. Comput..