Equiangular lines, mutually unbiased bases, and spin models

European Journal of Combinatorics

Volumn 30, Issue 1, 2009, Pages 246-262

  Godsil, Chris ^a   Roy, Aidan ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 53949091604     PISSN: 01956698     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejc.2008.01.002     Document Type: Article

References (26)

1. J.M. Renes, R. Blume-Kohout, A.J. Scott, C.M. Caves, Symmetric informationally complete quantum measurements, J. Math. Phys. 45 (2171)
2. G. Zauner, Quantendesigns - grundzüge einer nichtkommutativen designtheorie, Ph.D. Thesis, University of Vienna, 1999
3. M. Grassl, On SIC-POVMs and MUBs in dimension 6, in: Proceedings ERATO Conference on Quantum Information Science 2004, 2004, pp. 60-61
4. Appleby D.M. Symmetric informationally complete-positive operator valued measures and the extended Clifford group. J. Math. Phys. 46 5 (2005) 052107 29
5. Hoggar S.G. 64 lines from a quaternionic polytope. Geom. Dedicata 69 3 (1998) 287-289
6. König H. Cubature formulas on spheres. Advances in Multivariate Approximation (Witten-Bommerholz, 1998). Math. Res. vol. 107 (1999), Wiley-VCH, Berlin 201-211
7. 4-Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets. Proc. London Math. Soc. (3) 75 2 (1997) 436-480
8. Boykin P.O., Sitharam M., Tiep P.H., and Wocjan P. Mutually unbiased bases and orthogonal decompositions of lie algebras. Quantum Inf. Comput. 7 4 (2007) 371-382
9. Beth T., Jungnickel D., and Lenz H. Design Theory. 2nd ed. (1999), Cambridge University Press, Cambridge
10. Xia P., Zhou S., and Giannakis G.B. Achieving the Welch bound with difference sets. IEEE Trans. Inform. Theory 51 5 (2005) 1900-1907
11. Delsarte P., Goethals J.M., and Seidel J.J. Bounds for systems of lines and Jacobi polynomials. Philips Res. Rep. 30 (1975) 91-105
12. C. Godsil, Mutually unbiased bases and covers of complete bipartite graphs (in preparation)
13. Hughes D.R. Partial difference sets. Amer. J. Math. 78 (1956) 650-674
14. Cordero M., and Wene G.P. A survey of finite semifields. Discrete Math. 208/209 (1999) 125-137
15. Klappenecker A., and Rötteler M. Constructions of mutually unbiased bases. Finite Fields and Applications. Lecture Notes in Comput. Sci. vol. 2948 (2004), Springer, Berlin 137-144
16. Kantor W.M. On the inequivalence of generalized Preparata codes. IEEE Trans. Inform. Theory 29 3 (1983) 345-348
17. Kantor W.M. Commutative semifields and symplectic spreads. J. Algebra 270 1 (2003) 96-114
18. Alltop W.O. Complex sequences with low periodic correlations. IEEE Trans. Inform. Theory 26 3 (1980) 350-354
19. Wootters W.K., and Fields B.D. Optimal state-determination by mutually unbiased measurements. Ann. Physics 191 2 (1989) 363-381
20. Bandyopadhyay S., Boykin P.O., Roychowdhury V., and Vatan F. A new proof for the existence of mutually unbiased bases. Algorithmica 34 4 (2002) 512-528
21. Ivanović I.D. Geometrical description of quantal state determination. J. Phys. A 14 12 (1981) 3241-3245
22. Lidl R., and Niederreiter H. Finite Fields. 2nd ed. (1997), Cambridge University Press, Cambridge
23. Jones V.F.R. On knot invariants related to some statistical mechanical models. Pacific J. Math. 137 2 (1989) 311-334
24. Chan A., Godsil C., and Munemasa A. Four-weight spin models and Jones pairs. Trans. Amer. Math. Soc. 355 6 (2003) 2305-2325 electronic
25. Jaeger F. Strongly regular graphs and spin models for the Kauffman polynomial. Geom. Dedicata 44 1 (1992) 23-52
26. Nomura K. Spin models constructed from Hadamard matrices. J. Combin. Theory Ser. A 68 2 (1994) 251-261