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Entanglement and Its Multipartite Extensions

Profile image of Andreas OsterlohAndreas Osterloh

2013, International Journal of Modern Physics B

https://doi.org/10.1142/S0217979213450185
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24 pages

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Abstract

The aspects of many particle systems as far as their entanglement is concerned is highlighted. To this end we briefly review the bipartite measures of entanglement and the entanglement of pairs both for systems of distinguishable and indistinguishable particles. The analysis of these quantities in macroscopic systems shows that close to quantum phase transitions, the entanglement of many particles typically dominates that of pairs. This leads to an analysis of a method to construct many-body entanglement measures. SL-invariant measures are a generalization to quantities as the concurrence, and can be obtained with a formalism containing two (actually three) orthogonal antilinear operators. The main drawback of this antilinear framework, namely to measure these quantities in the experiment, is resolved by a formula linking the antilinear formalism to an equivalent linear framework.

Figures (2)
Fig. 1. Left panel: Bloch sphere for the two-dimensional space spanned by the GHZ state and the W state. The simplex So contains all states with zero threetangle. The leaves between po and pj represent sets of constant threetangle, and in the simplex 5S; the threetangle is affine. The corners of the simplices constitute the optimal decomposition. Right panel: Plot of the convex roofs of the tangle (solid line), concurrence (dashed line) and threetangle (dotted line). There is an interval with entangled states without concurrence or threetangle. From Ref. 102
Fig. 1. Left panel: Bloch sphere for the two-dimensional space spanned by the GHZ state and the W state. The simplex So contains all states with zero threetangle. The leaves between po and pj represent sets of constant threetangle, and in the simplex 5S; the threetangle is affine. The corners of the simplices constitute the optimal decomposition. Right panel: Plot of the convex roofs of the tangle (solid line), concurrence (dashed line) and threetangle (dotted line). There is an interval with entangled states without concurrence or threetangle. From Ref. 102
where G indicates the symmetrization with respect to the permutation group $4 on
where G indicates the symmetrization with respect to the permutation group $4 on

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References (111)

  1. J. Bell, Speakable and unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987).
  2. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
  3. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
  4. A. A. Methot and V. Scarani, J.Mod.Opt. 47, 355 (2000).
  5. M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Communication (Cambridge University Press, Cambridge, 2000).
  6. C. H. Bennett et al., Phys. Rev. Lett. 70, 1895 (1993).
  7. D. Bruß, J. Math. Phys. 43, 4237 (2002).
  8. I. Bengtsson and K. Zyczkowski, Geometry of Quantum States -An Introduction to Quantum Entanglement (Cambridge University Press, Cambridge, 2006).
  9. J. Eisert, quant-ph/0610253, PhD thesis, Univ. Potsdam, Germany.
  10. W. K. Wootters, Quant. Inf. Comp. 1, 27 (2001).
  11. M. Plenio and V. Vedral, Contemp. Phys. 39, 431 (1998).
  12. M. Plenio and S. Virmani, Quant. Inf. Comp. 7, 1 (2007).
  13. G. Vidal, J. Mod. Opt. 47, 355 (2000).
  14. C. H. Bennett et al., Phys. Rev. A 63, 012307 (2001).
  15. J. Preskill, J. Mod. Opt. 47, 127 (2000).
  16. S. Bose, Phys. Rev. Lett. 91, 207901 (2003).
  17. G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
  18. G. Vidal, Phys. Rev. Lett. 93, 040502 (2004).
  19. F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004).
  20. F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 104, 190405 (2010).
  21. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008).
  22. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).
  23. P. Lévay, Phys. Rev. A 71, 012334 (2004).
  24. P. Lévay, J. Phys. A 37, 1821 (2004).
  25. P. Lévay, J. Phys. A 38, 9075 (2005).
  26. P. Lévay, Phys. Rev. D 74, 024030 (2006).
  27. J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 74, 012313 (2006).
  28. P. Vrana and P. Lévay, J. Phys. A 42, 285303 (2009).
  29. L. Borsten et al., Phys. Rev. A 80, 032326 (2009).
  30. S. Virmani and M. B. Plenio, Physics Letters A 268, 31 (2000).
  31. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000).
  32. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997).
  33. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
  34. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
  35. T. J. Osborne and F. Verstraete, Phys. Rev. Lett. 96, 220503 (2006).
  36. C. H. Bennett, H. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996).
  37. C. H. Bennett, D. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
  38. M. B. Hastings, Nature Physics 5, 255 (2009).
  39. M. Fukuda, C. King, and D. K. Moser, Comm. Math. Phys. 296, 111 (2010).
  40. F. G. S. L. Brandao and M. Horodecki, Open Systems & Information Dynamics 17, 31 (2010).
  41. G. Vidal, W. Dür, and J. I. Cirac, Phys. Rev. Lett. 89, 027901 (2002).
  42. A. Fubini et al., Eur. Phys. J. D 38, 563 (2006).
  43. A. Uhlmann, Phys. Rev. A 62, 032307 (2000).
  44. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1997).
  45. G. Ghirardi, L. Marinatto, and T. Weber, J. Stat. Phys. 108, 49 (2002).
  46. G. Ghirardi and L. Marinatto, Fortschr. Phys. 51, 379 (2003).
  47. B. Groisman, S. Popescu, and A. Winter, Phys Rev A 72, 032317 (2005).
  48. A. Osterloh, arXiv:0810.1240; habilitation thesis, Univ. Hannover, Germany.
  49. J. Schliemann et al., Phys. Rev. A 64, 022303 (2001).
  50. J. Schliemann, D. Loss, and A. H. MacDonald, Phys. Rev. B 63, 085311 (2001).
  51. K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein, Ann. Phys. (NY) 299, 88 (2002).
  52. E. R. Caianello and S. Fubini, Nuovo Cimento 9, 1218 (1952).
  53. T. Muir, Treatise on the theory of determinants (Dover, New York, 1960).
  54. H. M. Wiseman, S. D. Bartlett, and J. A. Vaccaro, quant-ph/0309046, published in the proceedings of the 16th International Conference on Laser Spectroscopy (2003).
  55. F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 91, 010404 (2003).
  56. Y. S. Li, B. Zeng, X. S. Liu, and G. L. Long, Phys. Rev. A 64, 054302 (2001).
  57. R. Paškauskas and L. You, Phys. Rev. A 64, 042310 (2001).
  58. M. Kus and I. Bengtsson, Phys. Rev. A 80, 022319 (2009).
  59. T. Ichikawa, T. Sasaki, and I. Tsutsui, J. Math. Phys. 51, 062202 (2010).
  60. T. Sasaki, T. Ichikawa, and I. Tsutsui, Phys. Rev. A 83, 012113 (2011).
  61. J. Grabowski, M. Kus, and G. Marmo, J. Phys. A 44, 175302 (2011).
  62. J. Grabowski, M. Kus, and G. Marmo, J. Phys. A 45, 105301 (2012).
  63. P. Lévay and P. Vrana, Phys. Rev. A 78, 022329 (2008).
  64. P. Lévay, S. Nagy, and J. Pipek, Phys. Rev. A 72, 022302 (2005).
  65. G. Ghirardi and L. Marinatto, Optics and Spectroscopy 99, 386 (2005).
  66. C. V. Chianca and M. K. Olsen, Opt. Comm. 285, 825 (2012).
  67. A. Miyake and M. Wadati, Quant. Info. Comp. 2, 540 (2002).
  68. F. Verstraete, J. Dehaene, B. D. Moor, and H. Verschelde, Phys. Rev. A 65, 052112 (2002).
  69. E. Briand, J.-G. Luque, J.-Y. Thibon, and F. Verstraete, J. Math. Phys. 45, 4855 (2004).
  70. E. Briand, J.-G. Luque, and J.-Y. Thibon, J. Phys. A 36, 9915 (2003).
  71. A. Osterloh and J. Siewert, Phys. Rev. A 72, 012337 (2005).
  72. A. Osterloh and J. Siewert, Int. J. Quant. Inf. 4, 531 (2006).
  73. J.-G. Luque and J.-Y. Thibon, J. Phys. A 39, 371 (2005).
  74. A. Mandilara, V. M. Akulin, A. V. Smilga, and L. Viola, Phys Rev A 74, 022331 (2006).
  75. D. Ž. D -oković and A. Osterloh, J. Math. Phys. 50, 033509 (2009).
  76. D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002).
  77. H. Barnum, E. Knill, G. Ortiz, and L. Viola, Phys. Rev. A 68, 032308 (2003).
  78. A. J. Scott, Phys. Rev. A 69, 052330 (2004).
  79. T. R. de Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305 (2006).
  80. P. J. Love et al., Quant. Inf. Proc. 6, 187 (2007), quant-ph/0602143.
  81. T. R. de Oliveira, G. Rigolin, M. C. de Oliveira, and E. Miranda, Phys. Rev. Lett. 97, 170401 (2006).
  82. P. Facchi, G. Florio, and S. Pascazio, Phys. Rev. A 74, 042331 (2006).
  83. P. Facchi, G. Florio, and S. Pascazio, quant-ph/0610108 (unpublished).
  84. G. Costantini, P. Facchi, G. Florio, and S. Pascazio, J. Phys. A 40, 8009 (2007).
  85. M. G. Parker and V. Rijmen, in Sequences and Their Applications, SETA 2001, Discrete Mathematics and Theoretical Computer Science Series (Springer, 2001), quant-ph/0107106.
  86. T. C. Wei and P. M. Goldbart, Phys. Rev. A 68, 042307 (2003).
  87. A. Streltsov, H. Kampermann, and D. Bruss, Phys. Rev. A 84, 022323 (2011).
  88. O. Gühne, G. Toth, and H. J. Briegel, New J. Phys. 7, 229 (2005).
  89. S. S. Sharma and N. K. Sharma, Phys. Rev. A. 77, 042117 (2008), quant-ph/0608062.
  90. M. Hein, J. Eisert, and H. J. Briegel, Phys. Rev. A 69, 062311 (2004).
  91. K. Audenaert, F. Verstraete, , and B. De Moor, Phys. Rev. A. 64, 052304 (2001).
  92. P. Badziag et al., J. Mod. Opt. 49, 1289 (2002).
  93. P. Rungta et al., Phys. Rev. A 64, 042315 (2001).
  94. S. J. Akhtarshenas, J. Phys. A 38, 6777 (2005).
  95. F. Mintert, M. Kuś, and A. Buchleitner, Phys. Rev. Lett. 92, 167902 (2004).
  96. R. Demkowicz-Dobrzański, A. Buchleitner, M. Kuś, and F. Mintert, Phys. Rev. A 74, 052303 (2006).
  97. A. Wong and N. Christensen, Phys. Rev. A 63, 044301 (2001).
  98. A. Miyake, Phys. Rev. A 67, 012108 (2003).
  99. O. Chterental and D. Ž. D -oković, in Linear Algebra Research Advances (Nova Science, Hauppauge, N.Y., 2007), chap. 4, p. 133.
  100. F. Verstraete, J. Dehaene, and B. D. Moor, Phys. Rev. A 68, 012103 (2003).
  101. A. Osterloh and J. Siewert, New J. Phys. 12, 075025 (2010).
  102. R. Lohmayer, A. Osterloh, J. Siewert, and A. Uhlmann, Phys. Rev. Lett. 97, 260502 (2006).
  103. E. Jung, M.-R. Hwang, and J.-W. Son, Phys. Rev. A 79, 024306 (2009).
  104. H. Shu-Juan et al., Comm. Theor. Phys. 55, 251 (2011).
  105. O. Viehmann, C. Eltschka, and J. Siewert, Appl. Phys. B 106, 533 (2012), Spring Meeting of the German-Physical-Society, Dresden, GERMANY, 2011.
  106. C. Eltschka and J. Siewert, Phys. Rev. Lett. 108, 020502 (2012).
  107. J. Siewert and C. Eltschka, Phys. Rev. Lett. 108, 230502 (2012).
  108. O. Viehmann, C. Eltschka, and J. Siewert, Phys. Rev. A 83, 052330 (2011).
  109. L. Lamata, J. Leon, D. Salgado, and E. Solano, Phys. Rev. A 75, 022318 (2007).
  110. C. Eltschka, T. Bastin, A. Osterloh, and J. Siewert, Phys. Rev. A 85, 022301 (2012).
  111. J.-G. Luque and J.-Y. Thibon, Phys. Rev. A 67, 042303 (2003).

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