Wigner formula of rotation matrices and quantum walks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 1, 2007, Pages

  Miyazaki, Takahiro ^a   Katori, Makoto ^a   Konno, Norio ^b  

^a CHUO UNIVERSITY   (Japan)

^b YOKOHAMA NATIONAL UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; INTEGER PROGRAMMING; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBABILITY DENSITY FUNCTION; WAVE FUNCTIONS;

DIRAC'S DELTA FUNCTIONS; KONNO'S DENSITY FUNCTIONS; PROBABILITY DENSITIES; QUANTUM COINS;

RANDOM PROCESSES;

EID: 34547596490     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.012332     Document Type: Article

References (35)

1. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
2. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
3. R. Motwani and P. Raghavan, Randomized Algorithms (Cambridge University Press, Cambridge, England, 1995).
4. Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.48.1687 48, 1687 (1993).
5. D. A. Meyer, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02199356 85, 551 (1996).
6. A. Nayak and A. Vishwanath, e-print arXiv:quant-ph/0010117.
7. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (ACM Press, New York, 2001), pp. 37-49.
8. T. Oka, N. Konno, R. Arita, and H. Aoki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.100602 94, 100602 (2005).
9. N. Konno, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1023413713008 1, 345 (2002).
10. N. Konno, J. Math. Soc. Jpn. NISUBC 0025-5645 57, 1179 (2005).
11. G. Grimmett, S. Janson, and P. F. Scudo, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.026119 69, 026119 (2004).
12. L. K. Grover, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79. 325 79, 325 (1997).
13. A. Ambainis, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (IEEE, Piscataway, NJ, 2004), pp. 22-31.
14. J. Kempe, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107151031000110776 44, 307 (2003).
15. B. Tregenna, W. Flanagan, W. Maile, and V. Kendon, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/383 5, 83 (2003).
16. A. Ambainis, Int. J. Quantum Inf. ZZZZZZ 0219-7499 1, 507 (2003).
17. T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/12/304 35, 2745 (2002).
18. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052317 67, 052317 (2003).
19. V. M. Kendon, Int. J. Quantum Inf. ZZZZZZ 0219-7499 4, 791 (2006).
20. N. Konno, Fluct. Noise Lett. ZZZZZZ 0219-4775 5, L529 (2005).
21. A. D. Gottlieb, S. Janson, and P. F. Scudo, Infinite Dimen. Anal., Quantum Probab., Relat. Top. ZZZZZZ 0219-0257 8, 129 (2005).
22. N. Konno, Infinite Dimen. Anal., Quantum Probab., Relat. Top. ZZZZZZ 0219-0257 9, 287 (2006).
23. N. Obata, Infinite Dimen. Anal., Quantum Probab., Relat. Top. ZZZZZZ 0219-0257 9, 299 (2006).
24. N. Konno, Quantum Walks, Lecture at the School " Quantum Potential Theory: Structure and Applications to Physics " held at the Alfried Krupp Wissenschaftskolleg, Greifswald, 26 February-9 March 2007 (Reihe Mathematik, Ernst-Moritz-Arndt-Universität Greifswald, 2007).
25. M. Katori, S. Fujino, and N. Konno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012316 72, 012316 (2005).
26. N. Konno, e-print arXiv:quant-ph/0310191.
27. A. J. Bracken, D. Ellinas, and I. Smyrnakis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.022322 75, 022322 (2007).
28. H. Georgi, Lie Algebras in Particle Physics, 2nd ed. (Perseus Books, Reading, MA, 1999).
29. T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130602 91, 130602 (2003).
30. S. E. Venegas-Andraca, J. L. Ball, K. Burnett, and S. Bose, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/221 7, 221 (2005).
31. A. Messiah, Quantum Mechanics (North Holland, Amsterdam, 1962), Vol. II.
32. E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, 1959).
33. N. Inui and N. Konno, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.12. 060 353, 133 (2005).
34. N. Inui, N. Konno, and E. Segawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.056112 72, 056112 (2005).
35. N. Inui, Y. Konishi, and N. Konno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052323 69, 052323 (2004).