Information propagation through quantum chains with fluctuating disorder

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 5, 2009, Pages

  Burrell, Christian K ^a   Eisert, Jens ^b,c   Osborne, Tobias J ^a  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b UNIVERSITY OF POTSDAM   (Germany)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EXTERNAL FIELDS; FLUCTUATING FIELDS; INFORMATION PROPAGATION; NEAREST-NEIGHBOR INTERACTIONS; NEAREST-NEIGHBORS; QUANTUM CHAINS; QUANTUM SPIN CHAINS; XX CHAIN; Z-DIRECTIONS;

SPIN DYNAMICS;

EID: 70450250142     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.052319     Document Type: Article

References (21)

1. E. H. Lieb and D. W. Robinson, Commun. Math. Phys. 28, 251 (1972). 10.1007/BF01645779
2. B. Nachtergaele and R. Sims, Commun. Math. Phys. 265, 119 (2006). 10.1007/s00220-006-1556-1
3. M. B. Hastings, Phys. Rev. B 69, 104431 (2004). 10.1103/PhysRevB.69. 104431
4. T. J. Osborne, Phys. Rev. Lett. 97, 157202 (2006). 10.1103/PhysRevLett. 97.157202
5. M. B. Hastings, Phys. Rev. B 77, 144302 (2008). 10.1103/PhysRevB.77. 144302
6. C. K. Burrell and T. J. Osborne, Phys. Rev. Lett. 99, 167201 (2007). 10.1103/PhysRevLett.99.167201
7. M. Znidaric, T. Prosen, and P. Prelovsek, Phys. Rev. B 77, 064426 (2008). 10.1103/PhysRevB.77.064426
8. D. K. Burgarth, Ph.D. thesis, UCL, London, 2006.
9. S. Bose, Contemp. Phys. 48, 13 (2007). 10.1080/00107510701342313
10. D. Paquet and P. Leroux-Hugon, Phys. Rev. B 29, 593 (1984) 10.1103/PhysRevB.29.593
11. R. Leturcq, D. L'Hôte, R. Tourbot, C. J. Mellor, and M. Henini, Phys. Rev. Lett. 90, 076402 (2003) 10.1103/PhysRevLett.90.076402
12. P. C. Snijders, E. J. Moon, C. González, S. Rogge, J. Ortega, F. Flores, and H. H. Weitering, Phys. Rev. Lett. 99, 116102 (2007). 10.1103/PhysRevLett.99.116102
13. C. M. Caves and G. J. Milburn, Phys. Rev. A 36, 5543 (1987). 10.1103/PhysRevA.36.5543
14. D. Gross, K. Audenaert, and J. Eisert, J. Math. Phys. 48, 052104 (2007) 10.1063/1.2716992
15. C. Dankert, R. Cleve, J. Emerson, and E. Livine, e-print arXiv:quant-ph/0606161.
16. A. Harrow and R. Low, Comm. Math. Phys. 291, 257 (2009) 10.1007/s00220-009-0873-6
17. This can be shown by considering the differential equation in the coefficients of the Pauli operator basis, noting when the only fixed point corresponds to the maximally mixed state. One requires the following: let A be real and antisymmetric and E be a positive matrix, A= [BC - CT D], E= [00 0F]; if both F and C have maximum rank then Re [λj (A-E)] <0 for all j.
18. J. Billy, Nature (London) 453, 891 (2008). 10.1038/nature07000
19. We cannot calculate correlation functions directly for the first model as we do for the second, since our derivation requires the preservation of excitation number; neither can we calculate the Lieb-Robinson commutator for the latter as our calculation relies on the symmetry of the fluctuating fields.
20. P. Anderson, Phys. Rev. 109, 1492 (1958). 10.1103/PhysRev.109.1492
21. H. Buhrmann, in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (IEEE, Berkeley, CA, 2006), pp. 411-419. 10.1109/FOCS.2006.50