Symmetry-noise interplay in a quantum walk on an n -cycle

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 5, 2008, Pages

  Banerjee, Subhashish ^a,b   Srikanth, R ^a,c   Chandrashekar, C M ^d,e   Rungta, Pranaw ^f  

^a RAMAN RESEARCH INSTITUTE   (India)

^b CHENNAI MATHEMATICAL INSTITUTE   (India)

^c POORNAPRAJNA INSTITUTE OF SCIENTIFIC RESEARCH   (India)

^d UNIVERSITY OF WATERLOO   (Canada)

^e PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^f INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

TOPOLOGY;

AMPLITUDE DAMPING; CONDENSED MATTERS; GENERALIZED PHASE; N CYCLES; PHASE FLIPS; QUANTUM WALKS; SYMMETRY BREAKS; UNITARY TRANSFORMATIONS;

PROBABILITY DISTRIBUTIONS;

EID: 56249120948     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.052316     Document Type: Article

References (33)

1. M. N. Barber and B. W. Ninham, Random and Restricted Walks: Theory and Applications (Gordon and Breach, New York, 1970).
2. G. V. Riazanov, Sov. Phys. JETP 6, 1107 (1958);
3. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965);
4. Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A 48, 1687 (1993). 10.1103/PhysRevA.48.1687
5. A. Ambainis, J. Kempe, and A. Rivosh, Proceedings of ACM-SIAM SODA (ACM Press, New York, 2005).
6. D. A. Meyer, J. Stat. Phys. 85, 551 (1996); 10.1007/BF02199356
7. D. A. Meyer, Phys. Rev. E 55, 5261 (1997). 10.1103/PhysRevE.55.5261
8. C. A. Ryan, M. Laforest, J. C. Boileau, and R. Laflamme, Phys. Rev. A 72, 062317 (2005); 10.1103/PhysRevA.72.062317
9. J. Du, H. Li, X. Xu, M. Shi, J. Wu, X. Zhou, and R. Han, Phys. Rev. A 67, 042316 (2003). 10.1103/PhysRevA.67.042316
10. B. C. Travaglione and G. J. Milburn, Phys. Rev. A 65, 032310 (2002). 10.1103/PhysRevA.65.032310
11. W. Dür, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, Phys. Rev. A 66, 052319 (2002); 10.1103/PhysRevA.66.052319
12. K. Eckert, J. Mompart, G. Birkl, and M. Lewenstein, Phys. Rev. A 72, 012327 (2005); 10.1103/PhysRevA.72.012327
13. C. M. Chandrashekar, Phys. Rev. A 74, 032307 (2006). 10.1103/PhysRevA.74. 032307
14. C. M. Chandrashekar, R. Srikanth, and S. Banerjee, Phys. Rev. A 76, 022316 (2007). 10.1103/PhysRevA.76.022316
15. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973);
16. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
17. S. Banerjee and R. Ghosh, J. Phys. A 40, 13735 (2007). 10.1088/1751-8113/40/45/014
18. C. J. Myatt, Nature (London) 403, 269 (2000); 10.1038/35002001
19. Q. A. Turchette, C. J. Myatt, B. E. King, C. A. Sackett, D. Kielpinski, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. A 62, 053807 (2000). 10.1103/PhysRevA.62.053807
20. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
21. S. Banerjee and R. Srikanth, Eur. Phys. J. D 46, 335 (2008); 10.1140/epjd/e2007-00291-5
22. R. Srikanth and S. Banerjee, Phys. Rev. A 77, 012318 (2008). 10.1103/PhysRevA.77.012318
23. D. A. Meyer, J. Phys. A 34, 6981 (2001). 10.1088/0305-4470/34/35/323
24. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961).
25. U. Weiss, Quantum Dissipative Systems, 2nd ed. (World Scientific, Singapore, 1998).
26. J. Allinger and U. Weiss, Z. Phys. B: Condens. Matter 98, 289 (1995); 10.1007/BF01324535
27. D. Cohen, Phys. Rev. E 55, 1422 (1997). 10.1103/PhysRevE.55.1422
28. D. Forster, Hydrodynamic Fluctuations, Broken Symmetries, Correlation Functions (Benjamin, Reading, MA, 1975), Chap..
29. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998); 10.1103/PhysRevLett.81.3108
30. M. Greiner, Nature (London) 415, 39 (2002). 10.1038/415039a
31. C. M. Chandrashekar and R. Laflamme, Phys. Rev. A 78, 022314 (2008). 10.1103/PhysRevA.78.022314
32. V. Ambegaokar, U. Eckern, and G. Schon, Phys. Rev. Lett. 48, 1745 (1982); 10.1103/PhysRevLett.48.1745
33. U. Eckern, G. Schon, and V. Ambegaokar, Phys. Rev. B 30, 6419 (1984). 10.1103/PhysRevB.30.6419