Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 69, Issue 5 A, 2004, Pages

  Scott, A J ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHAOS THEORY; CODES (SYMBOLS); COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTATIONAL METHODS; DECODING; ENCODING (SYMBOLS); ERROR CORRECTION; LINEAR EQUATIONS; MATHEMATICAL MODELS; PARAMETER ESTIMATION;

MARGINAL DENSITY OPERATORS; QUANTUM EVOLUTIONS; QUANTUM KICKED ROTORS; QUANTUM-ERROR-CORRECTING CODES;

QUANTUM THEORY;

EID: 13444313990     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.69.052330     Document Type: Article

References (75)

1. M. Horodecki, Quantum Inf. Comput. 1, 3 (2001).
2. W. K. Wootters, Quantum Inf. Comput. 1, 27 (2001).
3. P. Horodecki and R. Horodecki, Quantum Inf. Comput. 1, 45 (2001).
4. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).
5. C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992).
6. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
7. W. Dur, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
8. C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. A 63, 012307 (2001).
9. J. Eisert and H. J. Briegel, Phys. Rev. A 64, 022306 (2001).
10. F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A 65, 052112 (2002).
11. F. Verstraete, J. Dehaene, and B. De Moor, Phys. Rev. A 68, 012103 (2003).
12. A. Miyake and M. Wadati, Quantum Inf. Comput. 2, 540 (2002).
13. A. Miyake, Phys. Rev. A 67, 012108 (2003).
14. G. Jaeger, M. Teodorescu-Frumosu, A. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 67, 032307 (2003).
15. M. Teodorescu-Frumosu and G. Jaeger, Phys. Rev. A 67, 052305 (2003).
16. G. Jaeger, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, Phys. Rev. A 68, 022318 (2003).
17. S. Bravyi, Phys. Rev. A 67, 012313 (2003).
18. A. Wong and N. Christensen, Phys. Rev. A 63, 044301 (2001).
19. D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002).
20. G. K. Brennen, Quantum Inf. Comput. 3, 619 (2003).
21. D. T. Pope and G. J. Milburn, Phys. Rev. A 67, 052107 (2003).
22. J. Preskill, Lecture notes for Physics 219: Quantum Computation (California Institute of Technology, Pasadena, CA, 1998); URL: http://www.theory.caltech.edu/people/preskill/ph219/
23. P. Zanardi, C. Zalka, and L. Faoro, Phys. Rev. A 62, 030301 (2000).
24. M. Sakagami, H. Kubotani, and T. Okamura, Prog. Theor. Phys. 95, 703 (1996).
25. A. Tanaka, J. Phys. A 29, 5475 (1996).
26. K. Furuya, M. C. Nemes, and G. Q. Pellegrino, Phys. Rev. Lett. 80, 5524 (1998).
27. R. M. Angelo, K. Furuya, M. C. Nemes, and G. Q. Pellegrino, Phys. Rev. E 60, 5407 (1999).
28. P. A. Miller and S. Sarkar, Phys. Rev. E 60, 1542 (1999).
29. A. Lakshminarayan, Phys. Rev. E 64, 036207 (2001).
30. J. N. Bandyopadhyay and A. Lakshminarayan, Phys. Rev. Lett. 89, 060402 (2002).
31. A. Tanaka, H. Fujisaki, and T. Miyadera, Phys. Rev. E 66, 045201 (2002).
32. H. Fujisaki, T. Miyadera, and A. Tanaka, Phys. Rev. E 67, 066201 (2003).
33. A. Lahiri and S. Nag, Phys. Lett. A 318, 6 (2003).
34. A. Lakshminarayan and V. Subrahmanyam, Phys. Rev. A 67, 052304 (2003).
35. S. Bettelli and D. L. Shepelyansky, Phys. Rev. A 67, 054303 (2003).
36. A. J. Scott and C. M. Caves, J. Phys. A 36, 9553 (2003).
37. J. N. Bandyopadhyay and A. Lakshminarayan, Phys. Rev. E 69, 016201 (2004).
38. P. Jacquod, Phys. Rev. Lett. 92, 150403 (2004).
39. D. Rossini, G. Benenti, and G. Casati, e-print quant-ph/0309146.
40. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
41. S. Popescu and D. Rohrlich, Phys. Rev. A 56, R3319 (1997).
42. C. M. Caves (private communication).
43. G. Vidai, J. Mod. Opt. 47, 355 (2000).
44. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, IEEE Trans. Inf. Theory 44, 1369 (1998).
45. D. Gottesman, Ph.D. thesis, California Institute of Technology, Pasadena CA, 1997.
46. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
47. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
48. M. Grassl, in Mathematics of Quantum Computation, edited by R. K. Brylinski and G. Chen (Chapman and Hall/CRC, London, 2002).
49. A. Klappenecker and M. Rötteler, in Mathematics of Quantum Computation, edited by R. K. Brylinski and G. Chen (Chapman and Hall/CRC, London, 2002).
50. E. M. Rains, IEEE Trans. Inf. Theory 45, 1827 (1999).
51. A. Klappenecker and M. Rötteler, IEEE Trans. Inf. Theory 48, 2392 (2002).
52. E. Knill, e-print quant-ph/9608048.
53. E. Knill, e-print quant-ph/9608049.
54. E. M. Rains, IEEE Trans. Inf. Theory 44, 1388 (1998).
55. P. Shor and R. Laflamme, Phys. Rev. Lett. 78, 1600 (1997).
56. E. M. Rains, IEEE Trans. Inf. Theory 45, 2361 (1999).
57. E. M. Rains, IEEE Trans. Inf. Theory 46, 54 (2000).
58. E. M. Rains, IEEE Trans. Inf. Theory 44, 134 (1998).
59. E. M. Rains and N. J. A. Sloane, in Handbook of Coding Theory, edited by V. S. Pless and W. C. Huffman (Elsevier, Amsterdam, 1998).
60. P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless, in Proceedings of the 37th Allerton Conference on Communication, Control and Computing, edited by B. Hajek and R. S. Sreenivas (Coordinated Science Laboratory UIUC, Urbana-Champaign, IL, 1999).
61. P. Gaborit, W. C. Huffman, J.-L. Kim, and V. Pless, in Codes and Association Schemes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, edited by A. Barg and S. Litsyn (American Mathematical Society, Providence, RI, 2001), Vol. 56.
62. G. Höhn, Math. Ann. 327, 227 (2003).
63. A. Ashikhmin and E. Knill, IEEE Trans. Inf. Theory 47, 3065 (2001).
64. D. Schlingemann and R. F. Werner, Phys. Rev. A 65, 012308 (2001).
65. K. Feng, IEEE Trans. Inf. Theory 48, 2384 (2002).
66. M. Grassl, T. Beth, and M. Rötteler, e-print quant-ph/0312164.
67. E. Lubkin, J. Math. Phys. 19, 1028 (1978).
68. W.-K. Tung, Group Theory in Physics (World Scientific, Singapore, 1985).
69. N. L. Balazs and A. Voros, Ann. Phys. (N.Y.) 190, 1 (1989).
70. M. Saraceno, Ann. Phys. (N.Y.) 199, 37 (1990).
71. R. Schack and C. M. Caves, Appl. Algebra Eng. Commun. Comput. 10, 305 (2000).
72. A. N. Soklakov and R. Schack, Phys. Rev. E 61, 5108 (2000).
73. M. M. Tracy and A. J. Scott, J. Phys. A 35, 8341 (2002).
74. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer, New York, 1992).
75. J. H. Hannay and M. V. Berry, Physica D 1, 267 (1980).