Infinite qubit rings with maximal nearest-neighbor entanglement: The Bethe ansatz solution

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 5, 2006, Pages

  Poulsen, U V ^a   Meyer, T ^b   Bruss D ^b   Lewenstein, M ^c,d  

^a AARHUS UNIVERSITY   (Denmark)

^b HEINRICH HEINE UNIVERSITY   (Germany)

^c INSTITUCIÓ CATALANA DE RECERCA I ESTUDIS AVANÇATS ICREA   (Spain)

^d LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING;

BETHE ANSATZ SOLUTION; ENTANGLEMENT; NEAREST-NEIGHBOR ENTANGLEMENT;

QUANTUM THEORY;

EID: 33744728679     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.052326     Document Type: Article

References (88)

1. For the theory, see, e.g., D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 81.3108 81, 3108 (1998);
2. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.1975 82, 1975 (1999);
3. J. K. Pachos and M. B. Plenio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.056402 93, 056402 (2004);
4. C. M. Alves and D. Jaksch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.110501 93, 110501 (2004).
5. For the experiments, see, e.g., O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, Nature (London) NATUAS 0028-0836 10.1038/nature02008 425, 937 (2003).
6. L.-M. Duan, A. Sørensen, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3991 85, 3991 (2000);
7. M. G. Moore and P. Meystre, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5026 85, 5026 (2000).
8. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
9. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
10. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003);
11. J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 10.1103/PhysRevLett.90.227902 4, 48 (2004).
12. J. Vidal, R. Mosseri, and J. Dukelsky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.054101 69, 054101 (2004);
13. L.-A. Wu, M. S. Sarandy, and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.250404 93, 250404 (2004);
14. L.-A. Wu, S. Bandyopadhyay, M. S. Sarandy, and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.032309 72, 032309 (2005);
15. M.-F. Yang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.030302 71, 030302 (R) (2005).
16. I. Bose and E. Chattopadhyay, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.062320 66, 062320 (2002);
17. A. Hutton and S. Bose, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69. 042312 69, 042312 (2004);
18. A. Hutton and S. Bose, e-print quant-ph/0408077;
19. M. Wieaäniak, V. Vedral, and Ä. Brukner, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/258 7, 258 (2005);
20. I. Bose and A. Tribedi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022314 72, 022314 (2005);
21. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. 1742-5468 (2005) P04010.
22. K. Audenaert, J. Eisert, M. B. Plenio, and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.042327 66, 042327 (2002).
23. U. V. Poulsen, T. Meyer, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.063605 71, 063605 (2005).
24. N. Schuch, J. I. Cirac, and M. M. Wolf, e-print quant-ph/0509166;
25. M. Cramer and J. Eisert, e-print quant-ph/0509167.
26. L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.34.373 34, 373 (1986);
27. M. Srednicki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71. 666 71, 666 (1993).
28. J. I. Latorre, R. Orus, E. Rico, and J. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.064101 71, 064101 (2005);
29. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. 1742-5468 (2004) P06002;
30. A. R. Its, B.-Q. Jin, and V. E. Korepin, J. Phys. A JPHAC5 0305-4470 38, 2975 (2005);
31. B.-Q. Jin and V. E. Korepin, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000037230.37166.42 116, 79 (2004);
32. J. P. Keating and F. Mezzadri, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.050501 94, 050501 (2005);
33. M. B. Plenio, J. Eisert, J. Dreissig, and M. Cramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060503 94, 060503 (2005);
34. M. Cramer, J. Eisert, M. B. Plenio, and J. Dreissig, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.012309 73, 012309 (2006).
35. W. Dür, L. Hartmann, M. Hein, M. Lewenstein, and H.-J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.097203 94, 097203 (2005).
36. F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.027901 92, 027901 (2004);
37. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087201 92, 087201 (2004).
38. M. Popp, F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042306 71, 042306 (2005).
39. D. Aharonov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062311 62, 062311 (2000).
40. S. Popescu and D. Rohrlich, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90711-T 166, 293 (1992).
41. A. Sen(De), U. Sen, M. Wieäniak, D. Kaszlikowski, and M. Żukowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.062306 68, 062306 (2003);
42. A. Sen(De), U. Sen, and M. Żukowski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032309 68, 032309 (2003).
43. B.-Q. Jin and V. E. Korepin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062314 69, 062314 (2004).
44. D. P. DiVincenzo, C. A. Fuchs, H. Mabuchi, J. A. Smolin, A. Thapliyal, and A. Uhlmann, e-print quant-ph/9803033;
45. O. Cohen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2493 80, 2493 (1998);
46. T. Laustsen, F. Verstraete, and S. J. van Enk, Quantum Inf. Comput. QICUAW 1533-7146 3, 64 (2003).
47. 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);
48. O. Gühne, G. Toth, and H.-J. Briegel, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/229 7, 229 (2005).
49. H.-J. Briegel and R. Raussendorf, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.910 86, 910 (2001);
50. R. Raussendorf and H.-J. Briegel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188 86, 5188 (2001).
51. L. Amico, A. Osterloh, F. Plastina, R. Fazio, and G. M. Palma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022304 69, 022304 (2004).
52. A. Sen(De), U. Sen, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.060304 70, 060304 (R) (2004).
53. S. Bose, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.207901 91, 207901 (2003).
54. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895 70, 1895 (1993).
55. R. Raussendorf, D. E. Browne, and H.-J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.022312 68, 022312 (2003);
56. M. A. Nielsen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93. 040503 93, 040503 (2004);
57. D. E. Browne and T. Rudolph, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010501 95, 010501 (2005).
58. V. Subrahmanyam, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.034304 69, 034304 (2004);
59. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.187902 92, 187902 (2004);
60. D. Burgarth and S. Bose, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052315 71, 052315 (2005);
61. S. Bose, B.-Q. Jin, and V. E. Korepin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022345 72, 022345 (2005);
62. D. Burgarth, V. Giovannetti, and S. Bose, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/30/013 38, 6793 (2005), and references therein.
63. A. Sen(De), U. Sen, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.052319 72, 052319 (2005).
64. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.040502 93, 040502 (2004);
65. F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227205 93, 227205 (2004);
66. F. Verstraete, J. J. Garcia-Ripoll, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207204 93, 207204 (2004);
67. M. Zwolak and G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.207205 93, 207205 (2004);
68. F. Verstraete and J. I. Cirac, e-print cond-mat/0407066;
69. C. Kollath, U. Schollwöck, J. von Delft, and W. Zwerger, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.053606 71, 053606 (2005);
70. for applications, see, for instance, S. R. Clark and D. Jaksch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.043612 70, 043612 (2004);
71. S. R. Clark and D. Jaksch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.043612 70, 043612 (2004);
72. A. J. Daley, S. R. Clark, D. Jaksch, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.043618 72, 043618 (2005).
73. W. K. Wootters, Contemp. Math. CTMAEH 0271-4132 305, 299 (2002);
74. K. M. O'Connor and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.052302 63, 052302 (2001);
75. W. K. Wootters, e-print quant-ph/0202048.
76. D. Bruß, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.4344 60, 4344 (1999).
77. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000).
78. T. Meyer, U. V. Poulsen, K. Eckert, M. Lewenstein, and D. Bruß, Int. J. Quantum Inf. 0219-7499 2, 149 (2004).
79. B. C. Hiesmayr, M. Koniorczyk, and H. Narnhofer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.032310 73, 032310 (2006).
80. M. M. Wolf, F. Verstraete, and J. I. Cirac, Int. J. Quantum Inf. 0219-7499 1, 465 (2003).
81. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
82. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, England, 1985), p. 414.
83. C. N. Yang and C. P. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.150.321 150, 321 (1966).
84. C. N. Yang and C. P. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.150.327 150, 327 (1966).
85. C. N. Yang and C. P. Yang, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.151.258 151, 258 (1966).
86. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1993).
87. J. D. Johnson, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.329593 52, 1991 (1981).
88. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed., (Cambridge University Press, Cambridge, 1992)