Entanglement generation and hamiltonian simulation in continuous-variable systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 4, 2003, Pages 423141-4231414

  Kraus, Barbara ^a   Hammerer, Klemens ^a   Giedke, Géza ^a   Cirac, J Ignacio ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; HAMILTONIANS; INFORMATION THEORY;

ENTANGLEMENT GENERATION;

QUANTUM THEORY;

EID: 4243371386     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Review

References (61)

1. A. Furusawa, J.L. Sørensen, S.L. Braunstein, C.A. Fuchs, H.J. Kimble, and E.S. Polzik, Science 282, 706 (1998).
2. L. Vaidman, Phys. Rev. A 49, 1473 (1994).
3. S.L. Braunslein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998).
4. J. Hald, J.L. Sørensen, C. Schori, and E.S. Polzik, Phys. Rev. Lett. 83, 1319 (1999).
5. B. Julsgaard, A. Kozhekin, and E.S. Polzik, Nature (London) 413, 400 (2000).
6. A. Kuzmich, L. Mandel, and N.P. Bigelow, Phys. Rev. Lett. 85, 1594 (2000).
7. A. Kuzmich and E.S. Polzik, Phys. Rev. Lett. 85, 5639 (2000).
8. L.-M. Duan, J.I. Cirac, P. Zoller, and E.S. Polzik, Phys. Rev. Lett. 85, 5643 (2000).
9. Quantum Information Theory with Continuous Variables, edited by S. L. Braunstein and A. K. Pati (Kluwer Academic,Dordrecht, 2002).
10. L.-M. Duan, G. Giedke, J. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
11. R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
12. R.F. Werner and M.M. Wolf, Phys. Rev. Lett. 86, 3658 (2001).
13. G. Giedke, B. Kraus, M. Lewenstein, and J.I. Cirac, Phys. Rev. Lett. 87, 167904 (2001).
14. G. Giedke, B. Kraus, M. Lewenstein, and J.I. Cirac, Phys. Rev. A 64, 052303 (2001).
15. G. Giedke, L.-M. Duan, P. Zoller, and J.I. Cirac, Quantum Inf. Comput. 1, 79 (2001).
16. G. Giedke and J.I. Cirac, Phys. Rev. A 66, 032316 (2002).
17. J. Eisert, S. Scheel, and M.B. Plenio, Phys. Rev. Lett. 89, 137903 (2002).
18. J. Fiurášek, Phys. Rev. Lett. 89, 137904 (2002).
19. L.K. Thomsen, S. Mancini, and H.M. Wiseman, J. Phys. B: At. Mol. Opt. Phys. 35, 4937 (2002).
20. I. Bouchoule and K. Mølmer, Phys. Rev. A 66, 043811 (2002).
21. A. Di Lisi and K. Mølmer, Phys. Rev. A 66, 052303 (2002).
22. D.W. Berry and B.C. Sanders, Phys. Rev. A 66, 012313 (2002).
23. W. Dur, G. Vidai, J.I. Cirac, N. Linden, and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001).
24. B. Kraus and J.I. Cirac, Phys. Rev. A 63, 062309 (2001).
25. P. Zanardi, C. Zalka, and L. Faoro, Phys. Rev. A 62, 030301 (R) (2000).
26. J.L. Dodd, M.A. Nielsen, M.J. Bremner, and R.T. Thew, Phys. Rev. A 65, 040301 (2002).
27. C.H. Bennett, A.W. Harrow, D.W. Leung, and J.A. Smolin, e-print quant-ph/0205057.
28. M.S. Leifer, L. Henderson, and N. Linden, e-print quant-ph/0205055.
29. P. Wocjan, M. Rötteler, D. Janzing, and T. Beth, J. Quant. Tnf. Comp. 2, 133 (2002).
30. M.A. Nielsen, M.J. Bremner, J.L. Dodd, A.M. Childs, and C.M. Dawson, e-print quant-ph/0109064.
31. G. Vidal and J.I. Cirac, Phys. Rev. A 66, 022315 (2002).
32. C.H. Bennett, J.I. Cirac, M.S. Leifer, D.W. Leung, N. Linden, S. Popescu, and G. Vidai, Phys. Rev. A 66, 012305 (2002).
33. G. Vidai, K. Hammerer, and J.I. Cirac, Phys. Rev. Lett. 88, 237902 (2002).
34. K. Hammerer, G. Vidai, and J.I. Cirac, Phys. Rev. A 66, 062321 (2002).
35. M.M. Wolf, J. Eisert, and M.B. Plenio, Phys. Rev. Lett. 90, 047904 (2003).
36. A. Kuzmich, N.P. Bigelow, and L. Mandel, Europhys. Lett. 42, 481 (1998).
37. K. Mølmer, Eur. Phys. J. D 5, 301 (1999).
38. E.S. Polzik, Phys. Rev. A 59, 4202 (1999).
39. Note that the Hamiltonians that we are considering here are not semibounded. However, this is not a problem since we are always considering initial states and times for which the real Hamiltonian can be locally approximated by these Hamiltonians.
40. C. Schori, B. Julsgaard, J.L. Sørensen, and E.S. Polzik, Phys. Rev. Lett. 89, 057903 (2002).
41. This is the case if the atomic ensemble is embedded in a ring cavity, for example. Note that for optically thick samples, the description may also be valid in free space.
42. L.-M. Duan, A. Sørensen, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 3991 (2000).
43. L.-M. Duan, J.I. Cirac, and P. Zoller, Phys. Rev. A 66, 023818 (2002).
44. T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940).
45. R. Schnabel, W.P. Bowen, N. Treps, T.C. Ralph, H.-A. Bachor, and P.K. Lam, e-print quant-ph/0208103.
46. R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
47. 1 =(trA)/(2 cosh r),cosh 2r2=(tr5)/(2 cosh r).
48. The sign function is defined as sign(x) = ±1 if x><0 and sign(x) = 0 if x = 0.
49. S. Lloyd and S.L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999).
50. G. Vidal and R.F. Werner, Phys. Rev. A 65, 032314 (2002).
51. 2) for the right-hand side in Eq. (15) as given by von Neumann's trace theorem [52].
52. R. A. Horn and C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1994).
53. t0 with respect to the evolution.
54. S.J. van Enk, Phys. Rev. A 60, 5095 (1999).
55. -2 = det A.
56. H. Scutaru, J. Math. Phys. 39, 6403 (1998).
57. R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1987).
58. A.E. Kozekhin, K. Mølmer, and E.S. Polzik, Phys. Rev. A 62, 033809 (2000).
59. M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993).
60. A. Sørensen, L.-M. Duan, J.I. Cirac, and P. Zoller, Nature (London) 409, 63 (2001).
61. S.L. Braunstein, e-print quant-ph/9904002.