Quantum entanglement via nilpotent polynomials

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 2, 2006, Pages

  Mandilara, Aikaterini ^a,b,c,d   Akulin, Vladimir M ^b,c,d   Smilga, Andrei V ^c,d   Viola, Lorenza ^d  

^a WASHINGTON UNIVERSITY   (United States)

^b CNRS   (France)

^c UNIVERSITÉ DE NANTES   (France)

^d Dartmouth College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; ELECTRON ENERGY LEVELS; EQUATIONS OF MOTION; POLYNOMIAL APPROXIMATION; VECTORS;

NILPOTENT POLYNOMIALS; QUANTUM ENTANGLEMENT; STATE VECTOR; VACUUM STATE;

QUANTUM THEORY;

EID: 33748665300     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.022331     Document Type: Article

References (81)

1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.47.777 47, 777 (1935).
2. E. Schrödinger, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 31, 555 (1935).
3. M. A. Nielsen and I. L. Chuang, Quantum Computation and Information (Cambridge University Press, Cambridge, England, 2000).
4. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895 70, 1895 (1993);
5. S. L. Braunstein, G. M. D'Ariano, G. J. Milburn, and M. F. Sacchi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.3486 84, 3486 (2000).
6. A. K. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.661 67, 661 (1991);
7. J. Kempe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.910 60, 910 (1999).
8. R. Jozsa and N. Linden, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 459, 2001 (2003).
9. R. Orus and J. I. Latorre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052308 69, 052308 (2004).
10. A. Tal and G. Kurizki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.160503 94, 160503 (2005);
11. T. Opatrny, B. Deb, and G. Kurizki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.250404 90, 250404 (2003).
12. B. Georgeot and D. L. Shepelyansky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.3504 62, 3504 (2000);
13. S. Bettelli and D. L. Shepelyansky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.054303 69, 054303 (2003).
14. C. Mejia-Monasterio, G. Benenti, G. G. Carlo, and G. Casati, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.062324 71, 062324 (2005).
15. L. F. Santos, G. Rigolin, and C. O. Escobar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.042304 69, 042304 (2004).
16. S. Montangero, G. Benenti, and R. Fazio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.187901 91, 187901 (2003);
17. S. Montangero and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.040302 73, 040302 (R) (2006).
18. M. C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.017901 87, 017901 (2001).
19. T. J. Osborne and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032110 66, 032110 (2002).
20. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902 90, 227902 (2003).
21. R. Eryigit, R. Eryigit, and Y. Gunduc, Int. J. Mod. Phys. C IJMPEO 0129-1831 15, 1095 (2004).
22. P. Stelmachovic and V. Buzek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.032313 70, 032313 (2004).
23. L. Amico, A. Osterloh, F. Plastina, R. Fazio, and G. M. Palma, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022304 69, 022304 (2004).
24. R. Somma, G. Ortiz, H. Barnum, E. Knill, and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.042311 70, 042311 (2004).
25. T.-C. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.060305 71, 060305 (R) (2005).
26. T. S. Cubitt, F. Verstraete, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.052308 71, 052308 (2005).
27. D. M. Greeberger, M. Horne, A. Shimony, and A. Zeilinger, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.16243 58, 1131 (1990).
28. W. Dur, G. Vidal, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.062314 62, 062314 (2000).
29. F. Verstraete, J. Dehaene, B. DeMoor, and H. Verschelde, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052112 65, 052112 (2002).
30. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
31. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998);
32. V. Coffman, J. Kundu, and W. K. Wooters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000).
33. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.2275 78, 2275 (1997).
34. D. A. Meyer and N. R. Wallach, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1497700 43, 4273 (2002).
35. A. Wong and N. Christensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.044301 63, 044301 (2001).
36. P. Rungta, V. Buzek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.042315 64, 042315 (2001).
37. C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.012307 63, 012307 (2001).
38. H. Heydari and G. Björk, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/39/012 37, 9251 (2004).
39. F. Verstraete, J. Dehaene, and B. De Moor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012103 68, 012103 (2003).
40. A. Acin, A. Andrianov, L. Costa, E. Jane, J. I. Latorre, and R. Tarrach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1560 85, 1560 (2000);
41. A. Acin, A. Andrianov, E. Jane, J. I. Latorre, and R. Tarrach, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/35/301 34, 6725 (2001).
42. A. Miyake, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.012108 67, 012108 (2003);
43. A. Miyake and F. Verstraete, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.012101 69, 012101 (2004).
44. M. Grassl, M. Rötteler, and T. Beth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.1833 58, 1833 (1998).
45. H. Barnum and N. Linden, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 34/35/305 34, 6787 (2001).
46. M. S. Leifer, N. Linden, and A. Winter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052304 69, 052304 (2004).
47. R. M. Gingrich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.052302 65, 052302 (2002).
48. A. Osterloh and J. Siewert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012337 72, 012337 (2005).
49. J. G. Luque and J. Y. Thibon, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.042303 67, 042303 (2003).
50. G. Vidal, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003400148268 47, 355 (2000).
51. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.2046 53, 2046 (1996).
52. J.-G. Luque and J.-Y. Thibon, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/2/007 39, 371 (2006).
53. H. A. Carteret, A. Higuchi, and A. Sudbery, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1319516 41, 7932 (2000).
54. T. A. Brun and O. Cohen, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01)00122-0 281, 88 (2001).
55. A. Sudbery, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/3/323 34, 643 (2001);
56. H. A. Carteret and A. Sudbery, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/28/303 33, 4981 (2000).
57. E. Briand, J.-G. Luque, and J.-Y. Thibon, J. Math. Phys. JMAPAQ 0022-2488 43, 4855 (2004).
58. N. Linden and S. Popescu, Fortschr. Phys. FPYKA6 0015-8208 10.1002/1521-3978(199806)46:4/5<567::AID-PROP567>3.0.CO;2-H 46, 567 (1998).
59. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022112 67, 022112 (2003).
60. F. A. Berezin, The Method of Second Quantization (Academic, Cambridge, 1966).
61. K. Efetov, Supersymmetry in Disorder and Chaos (Cambridge University Press, Cambridge, 1997).
62. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.3457 52, 3457 (1995);
63. S. Lloyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.346 75, 346 (1995).
64. J. L. Cereceda, quant-ph/0305043 (unpublished).
65. L.-B. Fu, J.-L. Chen, and X.-G. Zhao, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.022323 68, 022323 (2003).
66. H. Barnum, E. Knill, G. Ortiz, R. Somma, and L. Viola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.107902 92, 107902 (2004).
67. H. Barnum, E. Knill, G. Ortiz, and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032308 68, 032308 (2003).
68. S. J. Akhtarshenas, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/30/ 011 38, 6777 (2005).
69. K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1816 71, 1816 (1993).
70. D. M. Greenberger, M. Horne, and A. Zeilinger, in Bell's Theorem, Quantum Theory, and Conceptions of the Universe, edited by, M. Kafatos, (Kluwer, Dordrecht, 1989), pp. 69-72.
71. M. Saffman and T. G. Walker, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022347 72, 022347 (2005).
72. G. Molina-Terriza, A. Vaziri, J. Rehacek, Z. Hradil, and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.167903 92, 167903 (2004).
73. L. Viola, H. Barnum, E. Knill, G. Ortiz, and R. Somma, in Coding Theory and Quantum Computing, AMS Series in Contemporary Mathematics, Vol. 381, edited by, D. Evans, (Americal Mathematical Society, Providence, RI, 2005), pp. 117-130;
74. H. Barnum, G. Ortiz, R. Somma, and L. Viola, quant-ph/0506099.
75. J. F. Cornwell, Group Theory in Physics (Academic, San Diego, 1997).
76. J. E. Humphreys, Introduction to Lie Algebras and Representation Theory (Springer, New York, 1972).
77. A. M. Perelomov, Generalized Coherent States and their Applications (Springer, Berlin, 1986).
78. W.-M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62.867 62, 867 (1990).
79. R. Glauber, Phys. Rev. PHRVAO 0031-899X 131, 2766 (1963).
80. V. M. Akulin, Coherent Dynamics of Complex Quantum Systems (Springer, New York, 2005).
81. M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, Cambridge, 1999).