New construction of mutually unbiased bases in square dimensions

Quantum Information and Computation

Volumn 5, Issue 2, 2005, Pages 93-101

  Wocjan, Pawel ^a   Beth, Thomas ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Design theory; Latin squares; Mutually unbiased bases

Indexed keywords

COMPUTATIONAL METHODS; INFORMATION SYSTEMS;

ASYMPTOTIC GROWTH; DESIGN THEORY; LATIN SQUARE; LOWER BOUNDS; MUTUALLY ORTHOGONAL LATIN SQUARES; MUTUALLY UNBIASED BASIS; NEW CONSTRUCTIONS;

HADAMARD MATRICES;

EID: 16244391437     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. C. H. Bennett and G. Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of the IEEE Intl. Conf. Computers, Systems, and Signal Processing, pages 175-179, 1984.
2. D. Bruss. Optimal Eavesdropping in Quantum Cryptography with Six State. Phys. Rev. Lett., 81:3018-3021, 1998.
3. H. Bechmann-Pasquinucci and W. Tittel. Quantum cryptography using larger alphabets. Phys. Rev. A, 61(6):062308, 2000.
4. S. Bandyopadhyay, P. O. Boykin, V. Roychowdhury, and Vatan F. A new proof of the existence of mutually unbiased bases. Algorithmica, 34:512-528, 2002.
5. P. Delsarte, J. M. Goethals, and J. J. Seidel. Bounds for systems of lines, and Jacobi polynomials. Philips. Res. Repts., pages 91-105, 1975.
6. S. G. Hoggar. t-designs in projective spaces. Europ. J. Combin., 3:233-254, 1982.
7. G. A. Kabatiansky and V. I. Levenshtein. Bounds for packings on a sphere and in space. Problems of Information Transmission, 14(1):1-17, 1978.
8. W. K. Wootters and B. D. Fields. Optimal state-determination by mutually unbiased measurements. Ann. Physics, 191:363-381, 1989.
9. I. D. Ivanovic. Geometrical description of quantal state determination. J. Phys. A, 14:3241-3245, 1981.
10. K. S. Gibbons, M. J. Huffman, and W. K. Wootters. Discrete phase space based on finite fields. Preprint quant-ph/0401155, 2004.
11. L. Vaidman, Y. Aharonov, and D. Z. Albert. How to ascertain the values of σx, σy, and σz. Phys. Rev. Lett., 58:1385-1387, 1987.
12. B.-G. Englert and Y. Aharonov. The mean king's problem: Prime degrees of freedom. Phys. Letters, 284:1-5, 2001.
13. P. K. Aravind. Solution to the king's problem in prime dimensions. Z. Naturforschung, 58:2212, 2003.
14. G. Zauner. Quantendesigns - Grundzüge einer nichtkommutativen Designtheorie. Dissertation, Universität Wien, 1999.
15. A. Klappenecker and M. Rötteler. Constructions of mutually unbiased bases, in Finite Fields and Applications: 7th International Conference, Fq7, Mullen, Gary L. and Poli, A. and Stichtenoth, H. (eds.), Lecture Notes in Computer Science 2984, pages 137-144, 2003. See also preprint quant-ph/0309120.
16. M. Grassl. On SIC-POVMs and MUBs in dimension 6. Preprint quant-ph/0406175, accepted for presentation at EQIS 04, Tokyo, 2004.
17. Ch. J. Colbourn and J. H. Dinitz, editors. The CRC Handbook of Combinatorial Designs. CRC Press, Boca Raton FL, 1996.
18. A. S. Hedayat, N. J. A Sloane, and J. Stufken. Orthogonal Arrays. Springer Series in Statistics. Springer, 1999.
19. G. James and M. Liebeck. Representations and Characters of Groups. Cambridge, 2001.
20. Th. Beth, D. Jungnickel, and H. Lenz. Design Theory, volume I of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, 2nd edition, 1999.
21. Th. Beth, D. Jungnickel, and H. Lenz. Design Theory, volume II of Encyclopedia of Mathematics and Its Applications. Cambridge University Press, 2nd edition, 1999.
22. R. J. R. Abel, A. E. Brouwer, C. J. Colbourn, and J. H. Dinitz. chapter "Mutually orthogonal Latin squares (MOLS)", pages 111-142, in The CRC Handbook of Combinatorial Designs, Colbourn, C. J. and Dinitz, J. H. (eds.), CRC Press, 1996.
23. S. Chowla, P. Erdös, and E. G. Straus. On the maximal number of pairwise orthogonal Latin squares of a given order. Canadian J. Math., 12:204-208, 1960.
24. R. M. Wilson. Concerning the number of mutually orthogonal Latin squares. Discr. Math., 9:181-198, 1974.
25. Th. Beth. Eine Bemerkung zur Abschätzung der Anzahl orthogonaler lateinischer Quadrate mittels Siebverfahren. Abh. Math. Sem. Hamburg, 53:284-288, 1983.
26. Y. Chang. An estimate of the number of mutually orthogonal Latin squares. J. Comb. Math. Comb. Comput., 21:217-222, 1996.