Area laws in quantum systems: Mutual information and correlations

Physical Review Letters

Volumn 100, Issue 7, 2008, Pages

  Wolf, Michael M ^a   Verstraete, Frank ^b   Hastings, Matthew B ^c   Cirac, J Ignacio ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b UNIVERSITY OF VIENNA   (Austria)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HOLOGRAPHY;

AREA LAW; DEGREES OF FREEDOM; LATTICE MODELS; QUANTUM PHYSICS; THERMAL EQUILIBRIUM;

QUANTUM THEORY;

EID: 40849096540     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.100.070502     Document Type: Article

References (33)

1. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 416, 608 (2002). 10.1038/416608a
2. T.J. Osborne and M.A. Nielsen, Phys. Rev. A 66, 032110 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.032110
3. F. Verstraete, M. Popp, and J.I. Cirac, Phys. Rev. Lett. 92, 027901 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.027901
4. M. Plenio, J. Eisert, J. Dreißig, and M. Cramer, Phys. Rev. Lett. 94, 060503 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.060503
5. A. Botero and B. Reznik, Phys. Rev. A 70, 052329 (2004). PLRAAN 1050-2947 10.1103/PhysRevA.70.052329
6. H. Casini, C.D. Fosco, and M. Huerta, J. Stat. Mech. 1742-5468 (2005) P07007.
7. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902
8. B.-Q- Jin and V. Korepin, J. Stat. Phys. 116, 79 (2004). JSTPSB 0022-4715 10.1023/B:JOSS.0000037230.37166.42
9. P. Calabrese and J. Cardy, J. Stat. Mech. 1742-5468 (2004) P06002. 10.1088/1742-5468/2004/06/P06002
10. M.M. Wolf, Phys. Rev. Lett. 96, 010404 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.010404
11. D. Gioev and I. Klich, Phys. Rev. Lett. 96, 100503 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.100503
12. L. Bombelli, R.K. Koul, J.H. Lee, and R.D. Sorkin, Phys. Rev. D 34, 373 (1986). PRVDAQ 0556-2821 10.1103/PhysRevD.34.373
13. M. Sredniicki, Phys. Rev. Lett. 71, 666 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.666
14. G.'t Hooft, Nucl. Phys. NUPBBO 0550-3213 B256, 727 (1985). 10.1016/0550-3213(85)90418-3
15. C.G. Callan and F. Wilczek, Phys. Lett. B 333, 55 (1994). PYLBAJ 0370-2693 10.1016/0370-2693(94)91007-3
16. F. Verstraete and J.I. Cirac, arXiv:cond-mat/0407066.
17. G. Vidal, arXiv:cond-mat/0512165.
18. B. Groisman, S. Popescu, and A. Winter, Phys. Rev. A 72, 032317 (2005). PLRAAN 1050-2947 10.1103/PhysRevA.72.032317
19. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
20. M. Cramer, J. Eisert, M.B. Plenio, and J. Dreißig, Phys. Rev. A 73, 012309 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.73.012309
21. F. Verstraete, J.J. Garcia-Ripoll, and J.I. Cirac, Phys. Rev. Lett. 93, 207204 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.207204
22. See EPAPS Document No. E-PRLTAO-100-017808. This supplement proves: (i) every Gibbs state of a local quantum Hamiltonian with mutually commuting interactions is a mixed PEPS with small bond dimension, and (ii) finitely correlated states factorize exponentially. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
23. A.Y. Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003). APNYA6 0003-4916 10.1016/S0003-4916(02)00018-0
24. H.J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188
25. M.B. Hastings, Phys. Rev. B PRBMDO 0163-1829 73, 085115 (2006). 10.1103/PhysRevB.73.085115
26. M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer, Heidelberg, 1993).
27. P. Hayden, D. Leung, P.W. Shor, and A. Winter, Commun. Math. Phys. CMPHAY 0010-3616 250, 371 (2004); 10.1007/s00220-004-1087-6
28. M.B. Hastings, Phys. Rev. B PRBMDO 0163-1829 76, 035114 (2007); 10.1103/PhysRevB.76.035114
29. Ben-Aroya and Ta-Shma, arXiv:quant-ph/0702129.
30. F. Verstraete, M.M. Wolf, D. Perez-Garcia, and J.I. Cirac, Phys. Rev. Lett. 96, 220601 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.220601
31. M. Fannes, B. Nachtergaele, and R.F. Werner, Commun. Math. Phys. 144, 443 (1992). CMPHAY 0010-3616 10.1007/BF02099178
32. K.M.R. Audenaert, J. Phys. A JPHAC5 0305-4470 40, 8127 (2007). 10.1088/1751-8113/40/28/S18
33. P. Hayden, R. Jozsa, D. Petz, and A. Winter, Commun. Math. Phys. 246, 359 (2004). CMPHAY 0010-3616 10.1007/s00220-004-1049-z