Generalizations of entanglement based on coherent states and convex sets

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 3, 2003, Pages

  Barnum, Howard ^a   Knill, Emanuel ^a   Ortiz, Gerardo ^a   Viola, Lorenza ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; CONDENSATION; FERMIONS; GROUND STATE; MATHEMATICAL OPERATORS; PHASE TRANSITIONS; PHOTONS;

BIPARTITE QUANTUM SYSTEMS; CONVEX COMBINATION; HERMITITIAN CLOSED LIE ALGEBRA;

QUANTUM THEORY;

EID: 0242694954     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (85)

1. J.S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
2. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, UK, 1993).
3. J.F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
4. A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 47, 460 (1981).
5. M.A. Rowe, D. Kielpinski, V, Meyer, C.A. Sackett, W.M. Itano, C. Monroe, and D.J. Wineland, Nature (London) 409, 791 (2001).
6. C.H. Bennett, G. Brassard, C. Crepau, R. Jozsa, A. Peres, and W. Wooters, Phys. Rev. Lett. 70, 1895 (1993).
7. R. Raz, in Proceedings of the 31st Annual ACM Symposium on the Theory of Computation (STOC) (ACM Press, EL Paso, TX), pp. 358-367.
8. H. Buhrman, R. Cleve, and W.V. Dam, SIAM J. Comput. 30, 1829 (2000).
9. K. Grobe, K. Rzazewski, and J.H. Eberly, J. Phys. B 27, L503 (1994).
10. M.Y. Ivanov, D. Bitouk, and K. Rzazewski, Phys. Rev. A 52, 149 (1995).
11. J. Schliemann, D. Loss, and A.H. MacDonald, Phys. Rev. B 63, 085311 (1999).
12. J. Schliemann, J.I. Cirac, M. Kus, M. Lewenstein, and D. Loss, Phys. Rev. A 64, 022303 (2001).
13. R. Paskauskas and L. You, e-print quant-ph/0106117.
14. P. Zanardi, Phys. Rev. A 65, 042101 (2002).
15. P. Zanardi, and X. Wang, J. Phys. A 35, 7947 (2002).
16. Y. Shi, e-print quant-ph/0204058.
17. K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, Ann. Phys. (N.Y.) 299, 88 (2002).
18. Y. Shi, e-print quant-ph/0205069.
19. B. Yurke and D. Stoler, Phys. Rev. Lett. 57, 13 (1986).
20. B. Yurke and D. Stoler, Physica C 151, 298 (1988).
21. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1986).
22. R. Somma, G. Ortiz, J.E. Gubernatis, E. Knill, and R. Laflamme, Phys. Rev. A 65, 042323 (2002).
23. P. Zanardi, Phys. Rev. Lett. 87, 077901 (2001).
24. R. Gilmore, Rev. Mex. Fis. 23, 143 (1974).
25. A. Perelomov, Generalized Coherent States and their Applications (Springer, Berlin, 1985).
26. W.-M. Zhang, D.H. Feng, and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990).
27. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H.D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer Verlag, Berlin, 1996).
28. A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).
29. C. Cohen-Tannoudji, B. Diu, and F. Laloë Quantum Mechanics (Wiley, New York, 1977).
30. E. Schrödinger, Naturwissenshaften 23, 807 (1935); see Ref. [84].
31. E. Schrödinger, Proc. Cambridge Philos. Soc. 31, 555 (1935).
32. E.G. Beltrametti and S. Bugajski, J. Math. Phys. 38, 3020 (1997).
33. S. Gudder and S. Pulmannová, Comm. Math. Univ. Carol. 39, 645 (1998).
34. I. Namioka and R. Phelps, Pac. J. Math. 9, 469 (1969).
35. G. Wittstock, in Foundations of Quantum Mechanics and Ordered Linear Spaces, edited by H. Neumann, Springer Lecture Notes in Physics (Springer Verlag, New York, 1974).
36. A. Klyachko, e-print quant-ph/0206012.
37. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2001).
38. M.B. Plenio and V. Vedral, Contemp. Phys. 39, 431 (1998).
39. C. Brukner, M. Zukowski, and A. Zeilinger, e-print quant-ph/0106119.
40. M. Lewenstein, D. Bruss, J.I. Cirac, B. Kraus, M. Kus, J. Samsonowicz, A. Sanpera, and R. Tarrach, J. Mod. Opt. 47, 2481 (2000).
41. J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics Vol. 9 (Springer, New York, 1972).
42. V.S. Varadarajan, Lie Groups, Lie Algebras, and Their Representations, Graduate Texts in Mathematics Vol. 102 (Springer, New York, 1984).
43. W. Fulton and J. Harris, Representation Theory: A First Course, Graduate Texts in Mathematics Vol. 129 (Springer, New York, 1991).
44. A. Knapp, Lie Groups: Beyond an Introduction, 2nd ed. (Birkhäuser, Boston, 2001).
45. R. Gilmore, Lie Groups, Lie Algebras, and Some of Their Applications (Wiley, New York, 1973).
46. B.G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974).
47. J.F. Cornwell, Group Theory in Physics (Academic Press, London, 1989).
48. J. Fuchs and C. Schweigert, Symmetries, Lie Algebras, and Representations, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 1997).
49. H. Georgi, Lie Algebra in Particle Physics (Perseus Books, Reading, MA, 1999).
50. J. Hilger, K. H. Hoffman, and J.D. Lawson, Lie Groups, Convex Cones, and Semigroups (Clarendon Press, New York, 1989).
51. A. Barvinok http://www.math.lsa.umich.edu/barvinok/courses.html
52. R.F. Werner, Phys. Rev. A 40, 4277 (1989).
53. H. Ollivier and W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
54. C.H. Bennett, D.P. DiVincenzo, C.A. Fuchs, T. Mor, E. Rains, P.W. Shor, J.A. Smolin, and W.K. Wootters, Phys. Rev. A 59, 1070 (1999).
55. A. Abragam, Principles of Nuclear Magnetism (Clarendon Press, Oxford, England, 1961).
56. G. Vidal, J. Mod. Opt. 47, 355 (2000).
57. C.H. Bennett, S. Popescu, D. Rohrlich, J.A. Smolin, and A.V. Thapliyal, Phys. Rev. A 63, 012307 (2001).
58. W. Dür, G. Vidal, and J.I. Cirac, Phys. Rev. Lett. 89, 057901 (2002).
59. M.J. Donald, M. Horodecki, and O. Rudolph, J. Math. Phys. 43, 4252 (2002).
60. R. Bhatia, Matrix Analysis (Springer, New York, 1997).
61. H. Minc, Permanents (Addison-Wesley, Reading, MA, 1978).
62. C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, and W.K. Wooters, Phys. Rev. A 54, 3824 (1996).
63. C. Bennett, Phys. Scr. T76, 210 (1998).
64. J. Dixmier, Enveloping Algebras (American Mathematical Society Providence, RI, 1996).
65. R. Delbourgo, J. Phys. A 10, 1837 (1977).
66. R. Delbourgo and J.R. Fox, J. Phys. A 10, L233 (1977).
67. B.M. Terhal and D.P. DiVincenzo, Phys. Rev. A 65, 032325 (2002).
68. E. Knill, e-print quant-ph/0108033.
69. R. McWeeny, Methods of Molecular Quantum Mechanics (Academic Press, London, 1992).
70. A. Wilce, Int. J. Theor. Phys. 31, 1915 (1992).
71. L. Gurvits, e-print quant-ph/0201022.
72. F. Iachello and A. Arima, The Interacting Boson Model (Cambridge University Press, Cambridge, UK, 1987).
73. A. Barut, A. Bohm, and Y. Ne'eman, Dynamical Groups and Spectrum Generating Algebras (World Scientific, Singapore, 1988).
74. J.R. Schrieffer, Theory of Superconductivity (Perseus Books, Reading, MA, 1964).
75. C.D. Batista and G. Ortiz, Phys. Rev. B 67, 134301 (2003).
76. A. Lerda and S. Sciuto, Nucl. Phys. B 401, 613 (1993).
77. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 2001).
78. P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928).
79. C.D. Batista and G. Ortiz, Phys. Rev. Lett. 86, 1082 (2001).
80. T.J. Osborne and M.A. Nielsen, e-print quant-ph/0109024.
81. T.J. Osborne and M.A. Nielsen, Phys. Rev. A 66, 032110 (2002).
82. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) 416, 608 (2002).
83. J.K. Jain and R.K. Kamilla, Composite Fermions (World Scientific, Singapore, 1998), pp. 1-90.
84. E. Schrödinger, Proc. Am. Philos. Soc. 124, 323 (1980); refer to Ref. [85].
85. J.A. Wheeler and W.H. Zurek, Quantum Theory and Measurement (Princeton University Press, Princeton, 1983).