Mutually unbiased bases and orthogonal decompositions of Lie algebras

Quantum Information and Computation

Volumn 7, Issue 4, 2007, Pages 371-382

  Boykin, P Oscar ^a   Sitharam, Meera ^a   Tiep, Pham Huu ^b   Wocjan, Pawel ^c  

^a University of Florida   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Cartan subalgebras; Quantum computing; Quantum information processing; Special linear Lie algebra

Indexed keywords

COMPUTATION THEORY; DECOMPOSITION; EQUIVALENCE CLASSES; QUANTUM COMPUTERS;

LIE ALGEBRA; MUTUALLY UNBIASED BASIS; ORTHOGONAL DECOMPOSITION; QUANTUM COMPUTING; QUANTUM-INFORMATION PROCESSING; SUBALGEBRAS; UNITARY ERROR BASIS; UNITARY MATRIX;

ALGEBRA;

EID: 34247249418     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. M. Aschbacher, A. M. Childs, and P. Wocjan. Limitation of nice mutually unbiased bases, quant-ph/0412066, 2004.
2. S. Bandyopadhyay, P. O. Boykin, V. P. Roychowdhury, and F. Vatan. A new proof of the existence of mutually unbiased bases. Algorithmica, 34:512-528, 2002.
3. H. Bechmann-Pasquinucci and A. Peres. Quantum cryptography with 3-state Systems. Physical Review Letters, 85:3313, 2000. quant-ph/0001083.
4. P. O. Boykin and V. P. Roychowdhury. Information vs. disturbance in dimension d. Quantum Information and Computation, 5(5):396-412, 2005. quant-ph/0412028.
5. D. Bruss. Optimal eavesdropping in quantum cryptography with six states. Physical Review Letters, 81:3018-3021. 1998.
6. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin. Security of quantum key distribution using d-level systems. Physical Review Letters, 88:127902, 2002. quant-ph/0107130.
7. W. A. de Graaf. Lie Algebras: Theory and Algorithms. Elsevier, 2000.
8. P. de la Harpe and V. F. R. Jones. Paires de sous-algèbres semi-simples et graphes fortement réguliers. C. R. Acad. Sci. Paris Ser. I Math., 311:147-150, 1990.
9. K. S. Gibbons, M. J. Hoffman, and W. K. Wooters. Discrete phase space based on finite fields. Physical Review A, 70:062101, 2004.
10. C. Godsil and A. Roy. Equiangular lines, mutually unbiased bases, and spin models. arxiv:quant-ph/0511004.
11. I. D. Ivanovic. Geometrical description of quantal state determination. J. Phys. A, 14:3241-3245, 1981.
12. A. Klappenecker and M. Rötteler. Constructions of mutually unbiased bases. In Proc. International Conference on Finite Fields and Applications, pages 137-144, 2003.
13. A. Klappenecker and M. Rötteler. On the monomiality of nice error bases. Technical Report CORR 2003-04, Department of Combinatorics and Optimization, University of Waterloo, April 2003.
14. E. Knill. Non-binary unitary error bases and quantum codes. Technical Report LAUR-96-2717, Los Alamos National Laboratory, 1996.
15. n. Mat. Issled., 74, 1983 (in Russian).
16. A. I. Kostrikin and P. H. Tiep. Orthogonal Decompositions and Integral Lattices. de Gruyter Expositions in Mathematics 15. Walter de Gruyter, 1994.
17. O. Krueger and R. F. Werner. Some open problems in quantum information theory. quant-ph/0504166.
18. A. Munemasa and Y. Watatani. Paires orthogonales de sous-algebres involutives. C. R. Acad. Sci. Paris Ser. I Math., 314:329-331, 1992.
19. S. Popa. Orthogonal pairs of *-subalgebras in finite von neumann algebras. J. Operator Theory, 9:253-268, 1983.
20. 8. J. Algebra, 38:525-530, 1976.
21. 8(3). In Finite Groups Symposium, N. Iwahori ed., Japan Soc. for Promotion of Science, pages 113-116, 1976.
22. R. F. Werner. All teleportation and dense coding schemes. J. Phys. A, 34:7081-7094, 2001.
23. P. Wocjan and T. Beth. New construction of mutually unbiased bases in square dimensions. Quantum Information and Computation, 5(2):93-101, 2005.
24. W. K. Wootters and B. D. Fields. Optimal state-determination by mutually unbiased measurements. Ann. Physics, 191:363-381, 1989.