Asymptotic evolution of quantum walks on the N-cycle subject to decoherence on both the coin and position degrees of freedom

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 84, Issue 1, 2011, Pages

  Liu, Chaobin ^a   Petulante, Nelson ^a  

^a BOWIE STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC BEHAVIORS; ASYMPTOTIC DYNAMICS; ASYMPTOTIC EVOLUTION; ASYMPTOTICALLY STATIONARY; DECOHERENCE; DENSITY MATRIX; DISCRETE-TIME; EIGENSPACES; EIGENVALUES; EXPLICIT FORMULATION; INITIAL STATE; LIMITING BEHAVIOR; MIXED STATE; MUTUAL INFORMATIONS; QUANTUM WALK; UNITARY OPERATION;

EIGENVALUES AND EIGENFUNCTIONS; MECHANICS;

QUANTUM ENTANGLEMENT;

EID: 79961110770     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.84.012317     Document Type: Article

References (41)

1. A. M. Childs and J. Goldstone, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022314 70, 022314 (2004).
2. A. Ambainis, SIAM J. Comput. 0097-5397 10.1137/S0097539705447311 37, 210 (2007). (Pubitemid 351321994)
3. V. Potoček, A. Gábris, T. Kiss, and I. Jex, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.012325 79, 012325 (2009).
4. S. E. Venegas-Andraca, Quantum Walks for Computer Scientists, Synthesis Lectures on Quantum Computing (Morgan & Claypool, San Rafael, CA, 2008).
5. J. Kempe, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107151031000110776 44, 307 (2003). (Pubitemid 36937887)
6. N. Konno, in Quantum Potential Theory, Lecture Notes in Mathematics, edited by, U. Franz, and, M. Schurmann, (Springer-Verlag, Heidelberg, 2008), pp. 309-452.
7. G. Grimmett, S. Janson, and P. F. Scudo, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.69.026119 69, 026119 (2004).
8. H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber, and T. Schaetz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 103.090504 103, 090504 (2009).
9. F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, and C. F. Roos, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.100503 104, 100503 (2010).
10. M. Karski, L. Föster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede, and A. Widera, Science SCIEAS 0036-8075 10.1126/science.1174436 325, 174 (2009).
11. P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.052322 81, 052322 (2010).
12. A. Schreiber, K. N. Cassemiro, V. Potoček, A. Gábris, P. J. Mosley, E. Andersson, I. Jex, and C. Silberhorn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.050502 104, 050502 (2010).
13. M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru-Guzik, and A. G. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.153602 104, 153602 (2010).
14. T. A. Brun, H. A. Carteret and A. Ambainis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.032304 67, 032304 (2003).
15. V. Kendon and B. Tregenna, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.042315 67, 042315 (2003).
16. A. Romanelli, R. Siri, G. Abal, A. Auyuanet, and R. Donangelo, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.08.070 347, 137 (2005).
17. P. C. Richter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.042306 76, 042306 (2007). (Pubitemid 47531657)
18. S. Banerjee, R. Srikanth, C. M. Chandrashekar, and P. Rungta, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.052316 78, 052316 (2008).
19. C. Liu and N. Petulante, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.031113 81, 031113 (2010).
20. M. Annabestani, S. J. Akhtarshenas, and M. R. Abolhassani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.032321 81, 032321 (2010).
21. Y. Shikano, K. Chisaki, E. Segawa, and N. Konno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.062129 81, 062129 (2010).
22. V. Kendon, Math. Struct. Comput. Sci 17, 1169 (2006).
23. D. Aharanov, A. Ambainis, J. Kempe, and U. Vazirani, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (ACM, New York, 2001), pp. 50-59.
24. B. Tregenna, W. Flanagan, R. Maile, and V. Kendon, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/383 5, 83 (2003).
25. M. Bednarska, A. Grudka, P. Kurzyński, T. Åuczak, and A. Wójcik, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2003.08.023 317, 21 (2003).
26. N. Inui, Y. Konishi, N. Konno, and T. Soshi, Int. J. Quantum Inf. 0219-7499 10.1142/S0219749905001079 3, 535 (2005). (Pubitemid 44103129)
27. C. Liu and N. Petulante, Math. Struct. Comput. Sci. 0960-1295 10.1017/S096012951000040X 20, 1099 (2010).
28. O. Maloyer and V. Kendon, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/4/087 9, 87 (2007). (Pubitemid 46582145)
29. A. S. Holevo, Statistical Structure of Quantum Theory (Springer, Berlin, 2001).
30. K. Audenaert and S. Scheel, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/10/2/023011 10, 023011 (2008).
31. J. Novotný, G. Alber, and I. Jex, Cent. Eur. J. Phys. 1895-1082 10.2478/s11534-010-0018-8 8 (6), 1001 (2010).
32. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
33. D. Petz, Quantum Information Theory and Quantum Statistics, Theoretical and Mathematical Physics (Springer, Berlin/Heidelberg, 2008).
34. M. D. Choi, Lin. Alg. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75)90075-0 10, 285 (1975).
35. K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory (Springer Verlag, Berlin/New York, 1983).
36. J. Novotny, G. Alber, and I. Jex, J. Phys. A LAAPAW 1751-8113 10.1088/1751-8113/42/28/282003 42, 282003 (2009).
37. D. Pérez-García, M. M. Wolf, D. Petz and M. B. Ruskai, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2218675 47, 083506 (2006). (Pubitemid 44327396)
38. M. M. Wolf, Quantum Channels & Operations Guided Tour, online lecture notes [http://www.nbi.dk/~wolf/notes.pdf], September 12, 2010.
39. C. Liu and N. Petulante, e-print arXiv: 1010.0741.
40. J. Watrous, Theory of Quantum Information, Lecture notes from Fall 2008, Institute for Quantum Computing, University of Waterloo, Canada.
41. W. H. Zurek, in Decoherence Poincar e Í Seminar 2005, Progress in Mathematical Physics, edited by, Bertrand Duplantier, Jean-Michel Raimond, and, Vincent Rivasseau, (Birkhauser Verlag, Basel, 2006), pp. 1-31.