Entanglement-area law for general bosonic harmonic lattice systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 1, 2006, Pages

  Cramer, M ^a   Eisert, J ^a,b   Plenio, M B ^b   Dreissig J ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; ENTROPY; FUNCTIONS; MATRIX ALGEBRA; THERMAL EFFECTS;

BLOCK-BANDED MATRICES; BOSONIC HARMONIC LATTICE SYSTEMS; ENTANGLEMENT THEORY;

ELEMENTARY PARTICLES;

EID: 33144487612     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.012309     Document Type: Article

References (54)

1. S. J. Summers and R. F. Werner, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(85)90093-3 110A, 257 (1985).
2. P. Stelmachovic and V. Buzek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.032313 70, 032313 (2004).
3. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
4. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
5. 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).
6. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003);
7. J. I. Latorre, E. Rico, and G. Vidal, Quantum Inf. Comput. QICUAW 1533-7146 4, 048 (2004).
8. B.-Q. Jin and V. E. Korepin, J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000037230.37166.42 116, 79 (2004);
9. A. R. Its, B.-Q. Jin, and V. E. Korepin, J. Phys. A JPHAC5 0305-4470 10.1103/PhysRevLett.90.227902 38, 2975 (2005).
10. M. Fannes, B. Haegeman, and M. Mosonyi, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1623616 44, 6005 (2003).
11. M. B. Plenio, J. Eisert, J. Dreißig, and M. Cramer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060503 94, 060503 (2005).
12. J. Eisert and M. B. Plenio, Int. J. Quantum Inf. 0219-7499 1, 479 (2003).
13. M. B. Plenio and V. Vedral, Contemp. Phys. CTPHAF 0010-7514 10.1080/001075198181766 39, 431 (1998).
14. M. B. Plenio and S. Virmani, e-print quant-ph/0504163.
15. J. P. Keating and F. Mezzadri, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.050501 94, 050501 (2005);
16. J. P. Keating and F. Mezzadri, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-004-1188-2 252, 543 (2004).
17. P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. 1742-5468 (2004) p 06002.
18. M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062311 69, 062311 (2004).
19. J. K. Pachos and M. B. Plenio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.056402 93, 056402 (2004).
20. A. Hamma, R. Ionicioiu, and P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022315 71, 022315 (2005).
21. F. Verstraete and J. I. Cirac, e-print cond-mat/0407066.
22. M. M. Wolf, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087903 92, 087903 (2004).
23. A. Botero and B. Reznik, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.052329 70, 052329 (2004);
24. B. Reznik, A. Retzker, and J. Silman, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340410001664232 51, 833 (2004);
25. B. Reznik, Found. Phys. FNDPA4 0015-9018 10.1023/A:1022875910744 33, 167 (2003).
26. I. Peschel, J. Stat. Mech.: Theory Exp. 1742-5468 (2004) p 12005.
27. N. Lambert, C. Emary, and T. Brandes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.073602 92, 073602 (2004).
28. 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).
29. M. M. Wolf, e-print quant-ph/0503219.
30. D. Gioev and I. Klich, e-print quant-ph/0504151.
31. R. Orus, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052327 71, 052327 (2005).
32. J. I. Latorre, C. A. Lütken, E. Rico, and G. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.034301 71, 034301 (2005).
33. C. Callan and F. Wilczek, Phys. Lett. B PYLBAJ 0370-2693 10.1016/0370-2693(94)91007-3 333, 55 (1994).
34. J. D. Bekenstein, Lett. Nuovo Cimento Soc. Ital. Fis. LNUCAE 0375-930X 4, 737 (1972).
35. J. D. Bekenstein, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.7.2333 7, 2333 (1973).
36. J. D. Bekenstein, Contemp. Phys. CTPHAF 0010-7514 10.1080/ 00107510310001632523 45, 31 (2004).
37. 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).
38. M. Srednicki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71. 666 71, 666 (1993).
39. C. Holzhey, F. Larsen, and F. Wilczek, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90402-2 424, 443 (1995).
40. T. M. Fiola, J. Preskill, A. Strominger, and S. P. Trivedi, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.50.3987 50, 3987 (1994).
41. M. Cramer and J. Eisert, e-print quant-ph/0509167.
42. J. Cardy and I. Peschel, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(88)90604-9 300, 377 (1988).
43. K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998);
44. J. Eisert and M. B. Plenio, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003499150087 46, 145 (1999);
45. J. Eisert, Ph.D. thesis, University of Potsdam, 2001 (unpublished);
46. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002);
47. K. Audenaert, M. B. Plenio, and J. Eisert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.027901 90, 027901 (2003);
48. M. B. Plenio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 090503 95, 090503 (2005).
49. J. Eisert, C. Simon, and M. B. Plenio, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/17/307 35, 3911 (2002).
50. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, U.K., 1985).
51. I. Devetak and A. Winter, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.2004.1372 461, 207 (2005).
52. M. Benzi and G. H. Golub, BIT BITTEL 0006-3835 10.1023/A:1022362401426 39, 417 (1999).
53. A. Wehrl, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.50.221 50, 221 (1978).
54. D. J. E. Callaway, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.3738 53, 3738 (1996).