Freudenthal triple classification of three-qubit entanglement

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 80, Issue 3, 2009, Pages

  Borsten, L ^a   Dahanayake, D ^a   Duff, M J ^a   Rubens, W ^a   Ebrahim, H ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b BRANDEIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GREENBERGER-HORNE-ZEILINGER; JORDAN ALGEBRA; STOCHASTIC LOCAL OPERATIONS AND CLASSICAL COMMUNICATIONS; THREE-QUBIT ENTANGLEMENT; TRIPLE SYSTEM;

SEMICONDUCTOR QUANTUM DOTS;

EID: 70349479574     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.80.032326     Document Type: Article

References (65)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2000).
2. N. Linden and S. Popescu, Fortschr. Phys. 46, 567 (1998). 10.1002/(SICI)1521-3978(199806)46:4/5<567::AID-PROP567>3.0.CO;2-H
3. J. Kempe, Phys. Rev. A 60, 910 (1999). 10.1103/PhysRevA.60.910
4. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000). 10.1103/PhysRevA.62.062314 (Pubitemid 32076639)
5. A. Acín, A. Andrianov, L. Costa, E. Jané, J. I. Latorre, and R. Tarrach, Phys. Rev. Lett. 85, 1560 (2000). 10.1103/PhysRevLett.85.1560 (Pubitemid 30914797)
6. H. Carteret and A. Sudbery, J. Phys. A 33, 4981 (2000). 10.1088/0305-4470/33/28/303
7. A. Sudbery, J. Phys. A 34, 643 (2001). 10.1088/0305-4470/34/3/323
8. H. Carteret, A. Higuchi, and A. Sudbery, J. Math. Phys. 41, 7932 (2000). 10.1063/1.1319516
9. P. Lévay, Phys. Rev. A 71, 012334 (2005). 10.1103/PhysRevA.71. 012334
10. D. C. Brody, A. C. T. Gustavsson, and L. P. Hughston, J. Phys.: Conf. Ser. 67, 012044 (2007). 10.1088/1742-6596/67/1/012044
11. C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. A 63, 012307 (2000). 10.1103/PhysRevA.63.012307
12. D. Ž. Doković and A. Osterloh, J. Math. Phys. 50, 033509 (2009). 10.1063/1.3075830
13. A. Osterloh, e-print arXiv:0809.2055.
14. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000). 10.1103/PhysRevA.61.052306
15. A. Cayley, Camb. Math. J. 4, 193 (1845).
16. A. Miyake and M. Wadati, Quant. Info. Comp. 2, 540 (2002).
17. D. M. Greenberger, M. Horne, and A. Zeilinger, Bell's Theorem, Quantum Theory and Conceptions of the Universe (Kluwer Academic, Dordrecht, 1989).
18. T. A. Springer, Proc. K. Ned. Akad. Wet., Ser. A: Math. Sci. 24, 259 (1962).
19. K. McCrimmon, Trans. Am. Math. Soc. 139, 495 (1969). 10.2307/1995337
20. K. McCrimmon, A Taste of Jordan Algebras (Springer-Verlag, New York, 2004).
21. S. Krutelevich, J. Algebra 314, 924 (2007). 10.1016/j.jalgebra.2007.02. 060
22. N. Jacobson, Structure and Representations of Jordan Algebras (American Mathematical Society Colloquium Publications, Providence, 1968), Vol. 39.
23. N. Jacobson, J. Reine Angew. Math. 207, 61 (1961).
24. J. C. Baez, Bull., New Ser., Am. Math. Soc. 39, 145 (2001). 10.1090/S0273-0979-01-00934-X
25. R. Schafer, Introduction to Nonassociative Algebras (Academic Press, Inc., New York, 1966).
26. R. B. Brown, J. Reine Angew. Math. 236, 79 (1969).
27. H. Freudenthal, Proc. K. Ned. Akad. Wet., Ser. B: Phys. Sci. 57, 218 (1954).
28. J. R. Faulkner, Trans. Am. Math. Soc. 155, 397 (1971). 10.2307/1995694
29. C. J. Ferrar, Trans. Am. Math. Soc. 174, 313 (1972). 10.2307/1996111
30. M. J. Duff, Phys. Lett. B 641, 335 (2006). 10.1016/j.physletb.2006.08.050 (Pubitemid 44430239)
31. F. Toumazet, J. Luque, and J. Thibon, Math. Struct. Comp. Sci. 17, 1133 (2006).
32. L. Borsten, D. Dahanayake, M. J. Duff, H. Ebrahim, and W. Rubens, Phys. Rep. 471, 113 (2009). 10.1016/j.physrep.2008.11.002
33. N. Jacobson, Exceptional Lie Algebras (Marcel Dekker, Inc., New York, 1971).
34. M. Koecher, Am. J. Math. 89, 787 (1967). 10.2307/2373242
35. I. L. Kantor, Sov. Math. Dokl. 14, 254 (1973).
36. O. Shukuzawa, Commun. Algebra 34, 197 (2006). 10.1080/00927870500346206 (Pubitemid 43071075)
37. J. Gutt, e-print arXiv:0810.2138.
38. A. Miyake, Phys. Rev. A 67, 012108 (2003). 10.1103/PhysRevA.67.012108
39. I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants (Birkhäuser, Boston, 1994).
40. M. Günaydin, G. Sierra, and P. K. Townsend, Nucl. Phys. B 242, 244 (1984). 10.1016/0550-3213(84)90142-1
41. M. Günaydin, G. Sierra, and P. K. Townsend, Phys. Lett. B 133, 72 (1983). 10.1016/0370-2693(83)90108-9
42. M. Günaydin, G. Sierra, and P. K. Townsend, Nucl. Phys. B 253, 573 (1985). 10.1016/0550-3213(85)90547-4
43. S. Ferrara and J. M. Maldacena, Class. Quantum Grav. 15, 749 (1998). 10.1088/0264-9381/15/4/004 (Pubitemid 128054385)
44. S. Ferrara and M. Günaydin, Int. J. Mod. Phys. A 13, 2075 (1998). 10.1142/S0217751X98000913
45. B. Pioline, Class. Quant. Grav. 23, S981 (2006). 10.1088/0264-9381/23/21/ S05 (Pubitemid 44687381)
46. M. J. Duff, Phys. Rev. D 76, 025017 (2007). 10.1103/PhysRevD.76.025017
47. R. Kallosh and A. Linde, Phys. Rev. D 73, 104033 (2006). 10.1103/PhysRevD.73.104033 (Pubitemid 43788528)
48. P. Lévay, Phys. Rev. D 74, 024030 (2006). 10.1103/PhysRevD.74. 024030
49. S. Ferrara and R. Kallosh, Phys. Rev. D 73, 125005 (2006). 10.1103/PhysRevD.73.125005
50. M. J. Duff and S. Ferrara, Phys. Rev. D 76, 025018 (2007). 10.1103/PhysRevD.76.025018
51. P. Lévay, Phys. Rev. D 75, 024024 (2007). 10.1103/PhysRevD.75. 024024
52. M. J. Duff and S. Ferrara, Lect. Notes Phys. 755, 93 (2008)
53. Supersymmetric Mechanics (Springer, Berlin, 2008), Vol. 3, pp. 1-22.
54. S. Bellucci, S. Ferrara, and A. Marrani, e-print arXiv:hep-th/0702019.
55. M. J. Duff and S. Ferrara, Phys. Rev. D 76, 124023 (2007). 10.1103/PhysRevD.76.124023
56. S. Bellucci, A. Marrani, E. Orazi, and A. Shcherbakov, Phys. Lett. B 655, 185 (2007). 10.1016/j.physletb.2007.08.079
57. P. Lévay, Phys. Rev. D 76, 106011 (2007). 10.1103/PhysRevD.76. 106011
58. L. Borsten, D. Dahanayake, M. J. Duff, W. Rubens, and H. Ebrahim, Phys. Rev. Lett. 100, 251602 (2008). 10.1103/PhysRevLett.100.251602
59. S. Ferrara, K. Hayakawa, and A. Marrani, Fortschr. Phys. 56, 993 (2008). 10.1002/prop.200810569
60. L. Borsten, Fortschr. Phys. 56, 842 (2008). 10.1002/prop.200810542
61. P. Lévay and P. Vrana, Phys. Rev. A 78, 022329 (2008). 10.1103/PhysRevA.78.022329
62. S. Bellucci, S. Ferrara, A. Marrani, and A. Yeranyan, Entropy 10, 507 (2008). 10.3390/e10040507
63. P. Lévay, M. Saniga, and P. Vrana, Phys. Rev. D 78, 124022 (2008). 10.1103/PhysRevD.78.124022
64. L. Borsten, D. Dahanayake, M. J. Duff, and W. Rubens, Phys. Rev. D 80, 026003 (2009). 10.1103/PhysRevD.80.026003
65. S. Bellucci, S. Ferrara, M. Günaydin, and A. Marrani, Int. J. Mod. Phys. A 21, 5043 (2006). 10.1142/S0217751X06034355 (Pubitemid 44656167)