Mutually unbiased bases and Hadamard matrices of order six

Journal of Mathematical Physics

Volumn 48, Issue 5, 2007, Pages

  Bengtsson, Ingemar ^a   Bruzda, Wojciech ^b   Ericsson, Åsa ^a   Larsson, Jan Åke ^c   Tadej, Wojciech ^d   Zyczkowski, Karol ^b,e  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b JAGIELLONIAN UNIVERSITY   (Poland)

^c LINKÖPING UNIVERSITY   (Sweden)

^d Wydzia Matematyczno Przyrodniczy   (Poland)

^e CENTER FOR THEORETICAL PHYSICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34249870351     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2716990     Document Type: Article

References (32)

1. J. J. Sylvester, Philos. Mag. 34, 461 (1867).
2. M. J. Hadamard, Bull. Sci. Math. 17, 240 (1893).
3. I. D. Ivanović, J. Phys. A 14, 3241 (1981).
4. W. K. Wootters and B. D. Fields, Ann. Phys. (N.Y.) 191, 363 (1989).
5. S. Popa, J. Oper. Theory 9, 253 (1983).
6. A. I. Kostrikin, I. A. Kostrikin, and V. A. Ufnarovski, Proc. Steklov Inst. Math. 1983 (4), 113 (1983).
7. W. O. Alltop, IEEE Trans. Inf. Theory 26, 350 (1980).
8. A. R. Calderbank, P. J. Cameron, W. M. Kantor, and J. J. Seidel, Proc. London Math. Soc. 75, 436 (1997).
9. U. Haagerup, Operator Algebras and Quantum Field Theory, Rome (1996) (Internaty, Cambridge, MA, 1997).
10. P. Di, J. Phys. A 37, 5355 (2004).
11. W. Tadej and K. Zyczkowski, Open Syst. Inf. Dyn. 13, 133 (2006). For an updated on-line version of the catalogue of Hadamard matrices, see http://chaos.if.uj.edu.pl/~karol/hadamard.
12. W. Tadej and K. Zyczkowski, Open Syst. Inf. Dyn. 13, 133 (2006). For an updated on-line version of the catalogue of Hadamard matrices, see http://chaos.if.uj.edu.pl/~karol/hadamard.
13. G. Zauner, Ph.D. thesis, Universitat Wien, 1999.
14. A. I. Kostrikin and P. I. Tiep, Orthogonal Decompositions and Integral Lattices (de Gruyter Expositions in Mathematics, Berlin 1994).
15. M. Grassl, in Proceedings ERATO Conference on Quantum Information Science 2004, Tokyo, Sept. 5, 60 (2004).
16. G. Björck and R. Fröberg, J. Symb. Comput. 12, 329 (1991).
17. G. Björck and B. Saffari, C. R. Acad. Sci. Paris, Śr. I. 320, 319 (1995).
18. K. Beauchamp and R. Nicoara, e-print arXiv:math.OA/0609076.
19. G. E. Moorhouse, 2001 preprint available at http://www.uwyo.edu/ moorhouse/pub
20. T. Tao, Build. Services Eng. Res. Technol. 11, 251 (2004).
21. V. A. Ufnarovski, Mat. Issled. 90, 113 (1986) [in Russian; quoted by Kostrikin and Tiep, in the work cited].
22. I. Bengtsson and K. Zyczkowski, Geometry of Quantum States (Cambridge University Press, Cambridge, 2006).
23. J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Exp. Math. 5, 139 (1996).
24. P. A. Mello, J. Phys. A 23, 4061 (1990).
25. J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, J. Math. Phys. 45, 2171 (2004).
26. P. Wocjan and T. Beth, Quantum Inf. Comput. 5, 93 (2005).
27. A. Klappenecker and M. Rötteler, Proceedings of Seventh International Conference on finite fields and applications, Lecture Notes in Computer Science (Springer, New York, 2004), Vol. 2948.
28. K. Beauchamp and R. Nicoara (private communication).
29. M. Aschbacher, A. M. Childs and P. Wocjan, J. Algebr. Comb. 25, 111 (2007).
30. C. Archer, J. Math. Phys. 46, 022106 (2005).
31. M. Matolcsi and F. Szöllosi, e-print arXiv:math.CA/0702043.
32. W. Tadej, K. Zyczkowski, and W. Slomczynski, e-print arXiv:math.RA/ 0702510.