Incomplete pure dephasing of N-qubit entangled W states

Physical Review B - Condensed Matter and Materials Physics

Volumn 76, Issue 4, 2007, Pages

  Doll, Roland ^a   Wubs, Martijn ^a   Hänggi, Peter ^a   Kohler, Sigmund ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34447552416     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.76.045317     Document Type: Article

References (66)

1. Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Nature (London) NATUAS 0028-0836 10.1038/19718 398, 786 (1999).
2. D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, and M. H. Devoret, Science SCIEAS 0036-8075 10.1126/science.1069372 296, 886 (2002).
3. I. Chiorescu, Y. Nakamura, C. J. P. Harmans, and J. E. Mooij, Science SCIEAS 0036-8075 10.1126/science.1081045 299, 1869 (2003).
4. T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, Nature (London) NATUAS 0028-0836 10.1038/nature02015 425, 941 (2003).
5. G. M. Palma, K.-A. Suominen, and A. K. Ekert, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1996.0029 452, 567 (1996).
6. P. Zanardi and M. Rasetti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3306 79, 3306 (1997).
7. D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2594 81, 2594 (1998).
8. D. A. Lidar and K. B. Whaley, in Irreversible Quantum Dynamics, edited by, F. Benatti, and, R. Floreanini, (Springer, Berlin, 2003), pp. 83-120.
9. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.59.1 59, 1 (1987).
10. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62.251 62, 251 (1990).
11. M. Grifoni and P. Hänggi, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00022-2 304, 229 (1998).
12. C. W. Gardiner, Quantum Noise, Vol. 56 of Springer Series in Synergetics (Springer, Berlin, 1991).
13. T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger, Quantum Transport and Dissipation (Wiley-VCH, Weinheim, 1998).
14. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
15. P. Borri, W. Langbein, S. Schneider, U. Woggon, R. L. Sellin, D. Ouyang, and D. Bimberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.157401 87, 157401 (2001).
16. D. Mozyrsky, S. Kogan, V. N. Gorshkov, and G. P. Berman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.245213 65, 245213 (2002).
17. E. A. Muljarov and R. Zimmermann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.237401 93, 237401 (2004).
18. J. Luczka, Physica A PHYADX 0378-4371 10.1016/0378-4371(90)90299-8 167, 919 (1990).
19. N. G. van Kampen, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF02183350 78, 299 (1995).
20. W. G. Unruh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.992 51, 992 (1995).
21. L.-M. Duan and G.-C. Guo, Quantum Semiclassic. Opt. QUSOEC 1355-5111 10.1088/1355-5111/10/4/004 10, 611 (1998).
22. B. Krummheuer, V. M. Axt, and T. Kuhn, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.195313 65, 195313 (2002).
23. T. Yu and J. H. Eberly, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.193306 66, 193306 (2002).
24. T. Yu and J. H. Eberly, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.165322 68, 165322 (2003).
25. D. Solenov, D. Tolkunov, and V. Privman, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.035134 75, 035134 (2007).
26. R. Doll, M. Wubs, P. Hänggi, and S. Kohler, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10326-y 76, 547 (2006).
27. In recent literature (Refs.), the term " robust entanglement " also has also been used with a different meaning, namely, for the entanglement of a N -qubit state that becomes a (N-1) -qubit entangled state after tracing out one qubit.
28. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
29. J. Joo, Y.-J. Park, S. Oh, and J. Kim, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/5/1/136 5, 136 (2003).
30. P. Agrawal and A. Pati, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.062320 74, 062320 (2006).
31. Y.-J. Han, Y.-S. Zhang, and G.-C. Guo, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00168-8 295, 61 (2002).
32. M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.077901 92, 077901 (2004).
33. C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, Science SCIEAS 0036-8075 10.1126/science.1097522 304, 1478 (2004).
34. H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.150404 95, 150404 (2005).
35. H. Häffner, W. Hänsel, C. F. Roos, J. Benhelm, D. Chek-al-kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, and R. Blatt, Nature (London) NATUAS 0028-0836 10.1038/nature04279 438, 643 (2005).
36. V. N. Gorbachev, A. A. Rodichkina, A. I. Trubilko, and A. I. Zilba, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(03)00404-3 310, 339 (2003).
37. D. Bruss, N. Datta, A. Ekert, L. C. Kwek, and C. Macchiavello, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.014301 72, 014301 (2005).
38. K. Saito, M. Wubs, S. Kohler, P. Hänggi, and Y. Kayanuma, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10232-4 76, 22 (2006).
39. M. Wubs, S. Kohler, and P. Hänggi, Physica E, doi: 10.1016/j.physe.2007.05.014 (2007).
40. K. Blum, Density Matrix Theory and Applications 2nd ed. (Plenum Press, New York, 1996).
41. A. R. R. Carvalho, F. Mintert, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.230501 93, 230501 (2004).
42. C. Simon and J. Kempe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65. 052327 65, 052327 (2002).
43. W. Dür and H.-J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.180403 92, 180403 (2004).
44. Note that the expression for Λm,n (t) in Ref. contains a misprint. The correct expression is Eq. 9.
45. L. Fedichkin and V. Privman, in Electron Spin Resonance and Related Phenomena in Low Dimensional Structures, edited by, M. Fanciulli, (Springer, Berlin, 2007).
46. T. Brandes and T. Vorrath, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.075341 66, 075341 (2002).
47. L. Fedichkin and A. Fedorov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.032311 69, 032311 (2004).
48. S. Vorojtsov, E. R. Mucciolo, and H. U. Baranger, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.205322 71, 205322 (2005).
49. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
50. K. Roszak and P. Machnikowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022313 73, 022313 (2006).
51. J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.390 78, 390 (1997).
52. M. A. Nielsen and I. L. Chuang, Quantum Computing and Quantum Information (Cambridge University Press, Cambridge, 2000).
53. F. Mintert, A. R. R. Carvalho, M. Kuś, and A. Buchleitner, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.04.006 415, 207 (2005).
54. R. Lohmayer, A. Osterloh, J. Siewert, and A. Uhlmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.260502 97, 260502 (2006).
55. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, e-print arXiv:quant-ph/0702225 (unpublished).
56. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 2001).
57. Y. C. Cheng and R. J. Silbey, J. Phys. Chem. B JPCBFK 1089-5647 10.1021/jp051303o 109, 21399 (2005).
58. R. Klesse and S. Frank, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.230503 95, 230503 (2005).
59. B. M. Terhal and G. Burkard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.012336 71, 012336 (2005).
60. P. Aliferis, D. Gottesman, and J. Preskill, Quantum Inf. Comput. QICUAW 1533-7146 6, 97 (2006).
61. R. I. Karasik, K.-P. Marzlin, B. C. Sanders, and K. B. Whaley, arXiv:cond-mat/0702244 (unpublished).
62. J. H. Reina, L. Quiroga, and N. F. Johnson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032326 65, 032326 (2002).
63. S. Nakajima, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.20.948 20, 948 (1958).
64. R. Zwanzig, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1731409 33, 1338 (1960).
65. R. Kubo, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.17.1100 17, 1100 (1962).
66. N. G. van Kampen, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/0031-8914(74)90121-9 74, 215 (1974).