Detection of multipartite entanglement in the vicinity of symmetric Dicke states

Journal of the Optical Society of America B: Optical Physics

Volumn 24, Issue 2, 2007, Pages 275-282

  Tóth, Géza ^a,b  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT LIGHT; PHOTOEXCITATION;

COLLECTIVE SPIN OPERATORS; MULTIPARTITE ENTANGLEMENT; SPIN SQUEEZING CRITERION; SYMMETRIC DICKE STATES;

QUANTUM OPTICS;

EID: 33847066559     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.24.000275     Document Type: Article

References (61)

1. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 47, 777-780 (1935).
2. R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Phys. Rev. A 40, 4277-4281 (1989).
3. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, "Experimental entanglement of four particles," Nature 404, 256-259 (2000).
4. A. Acín, D. Bruss, M. Lewenstein, and A. Sanpera, "Classification of mixed three-qubit states," Phys. Rev. Lett. 87, 040401 (2001).
5. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000).
6. J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, "Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement," Nature 403, 515-519 (2000).
7. D. Bouwmeester, A. Ekert, and A. Zeilinger, The Physics of Quantum Information (Springer, 2000), p. 209.
8. Z. Zhao, T. Yang, Y.-A. Chen, A.-N. Zhang, M. Zukowski, and J.-W. Pan, "Experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger entanglement," Phys. Rev. Lett. 91, 180401 (2003).
9. Z. Zhao, Y.-A. Chen, A.-N. Zhang, T. Yang, H. J. Briegel, and J.-W. Pan, "Experimental demonstration of five-photon entanglement and open-destination teleportation," Nature 430, 54-58 (2004).
10. M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruss, M. Lewenstein, and A. Sanpera, "Experimental detection of multipartite entanglement using witness operators," Phys. Rev. Lett. 92, 087902 (2004).
11. P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, and A. Zeilinger, "Experimental one-way quantum computing," Nature 434, 169-176 (2005).
12. P. Walther. M. Aspelmeyer, K. J. Resch, and A. Zeilinger, "Experimental violation of a cluster state Bell inequality," Phys. Rev. Lett. 95, 020403 (2005).
13. N. Kiesel, C. Schmid, U. Weber, O. Gühne, G. Tóth, R. Ursin, and H. Weinfurter, "Experimental analysis of a four-qubit photon cluster state," Phys. Rev. Lett. 95, 210502 (2005).
14. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, "Controlled collisions for multi-particle entanglement of optically trapped atoms," Nature 425, 937-940 (2003).
15. D. M. Greenberger, M. A. Home, A. Shimony, and A. Zeilinger, "Bell's theorem without inequalities," Am. J. Phys. 58, 1131-1143 (1990).
16. H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Phys. Rev. Lett. 86, 910-913 (2001).
17. R. Raussendorf and H. J. Briegel, "A one-way quantum computer," Phys. Rev. Lett. 86, 5188-5191 (2001).
18. M. Eibl, S. Gaertner, M. Bourennane, C. Kurtsiefer, M. Zukowski, and H. Weinfurter, "Experimental observation of four-photon entanglement from parametric downconversion," Phys. Rev. Lett. 90, 200403 (2003).
19. R. H. Dicke, "Coherence in spontaneous radiation processes," Phys. Rev. 93, 99-110 (1954).
20. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, "Characterizing the entanglement of symmetric many-particle spin-1/2 systems," Phys. Rev. A 67, 022112 (2003).
21. R. G. Unanyan and M. Fleischhauer, "Decoherence-free generation of many-particle entanglement by adiabatic ground-state transitions," Phys. Rev. Lett. 90, 133601 (2003).
22. L.-M. Duan and H. J. Kimble, "Efficient engineering of multiatom entanglement through single-photon detections," Phys. Rev. Lett. 90, 253601 (2003).
23. A. Retzker, E. Solano, and B. Reznik, "Tavis-Cummings model and collective multi-qubit entanglement in trapped ions," http:// www.arxiv.org/quant-ph/0605048.
24. J. K. Stockton, R. van Handel, and H. Mabuchi, "Deterministic Dicke-state preparation with continuous measurement and control," Phys. Rev. A 70, 022106 (2004).
25. X. Zou, K. Pahlke, and W. Matins, "Generation of arbitrary superpositions of the Dicke states of excitons in optically driven quantum dots," Phys. Rev. A 68, 034306 (2003).
26. Y-F. Xiao, Z.-F. Han, J. Gao, and G.-C. Guo, "Generation of multi-atom Dicke states with quasi-unit probability through the detection of cavity decay," http://www.arxiv.org/quant-ph/0412202.
27. V. N. Gorbachev and A. I. Trubilko, "On multiparticle W states, their implementations and application in the quantum informational problems," Laser Phys. Lett. 3, 59-70 (2006).
28. M. Eibl, N. Kiesel, A Bourennane, C. Kurtsiefer, and H. Weinfurter, "Experimental realization of a three-qubit entangled W state," Phys. Rev. Lett. 92, 077901 (2004).
29. H. Mikami, Y. Li, K. Fukuoka, and T. Kobayashi, "New high-efficiency source of a three-photon W state and its full characterization using quantum state tomography," Phys. Rev. Lett. 95, 150404 (2005).
30. H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. Chek-alkar, M. Chwalla, T. Körber, U. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W Dür, and R. Blatt, "Scalable multiparticle entanglement of trapped ions," Nature 438, 643-646 (2005).
31. N. Kiesel, C. Schmid, G. Tóth, E. Solano, and H. Weinfurter, "Experimental observation of four-photon entangled Dicke state with high fidelity," http://www.arxiv.org/quant-ph/0606234.
32. A. Sørensen and K. Mølmer, "Spin-spin interaction and spin squeezing in an optical lattice," Phys. Rev. Lett. 83, 2274-2277 (1999).
33. A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, "Manyparticle entanglement with Bose-Einstein condensates," Nature 409, 63-66 (2001).
34. A. Sørensen and K. Mølmer, "Entanglement and extreme spin squeezing," Phys. Rev. Lett. 86, 4431-4434 (2001).
35. X. G. Wang, A. Sørensen, and K. Mølmer, "Spin squeezing in the Ising model," Phys. Rev. A 64, 053815 (2001).
36. G. Tóth, "Entanglement detection in optical lattices of bosonic atoms with collective measurements," Phys. Rev. A 69, 052327 (2004).
37. J. Korbicz, J. I. Cirac, and M. Lewenstein, "Spin squeezing inequalities and entanglement of N qubit states," Phys. Rev. Lett. 95, 120502 (2005).
38. J. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C. F. Roos, and R. Blatt, "Generalized spin squeezing inequalities in N qubit systems: theory and experiment," http://www.arxiv.org/ quant-ph/0601038.
39. A Horodecki, P. Horodecki, and R. Horodecki, "Separability of mixed states: necessary and sufficient conditions," Phys. Lett. A 223, 1-8 (1996).
40. B. M. Terhal, "Bell inequalities and the separability criterion," Phys. Lett. A 271, 319-326 (2000).
41. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, "Optimization of entanglement witnesses," Phys. Rev. A 62, 052310 (2000).
42. D. Bruss, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, "Reflections upon separability and distillability," J. Mod. Opt. 49, 1399-1418 (2002).
43. K. Chen and L.-A. Wu, "Test for entanglement using physically observable witness operators and positive maps," Phys. Rev. A 69, 022312 (2004).
44. S. Yu and N. Liu, "Entanglement detection by local orthogonal observables," Phys. Rev. Lett. 95, 150504 (2005).
45. L.-A. Wu, S. Bandyopadhyay, M. S. Sarandy, and D. A. Lidar, "Entanglement observables and witnesses for interacting quantum spin systems," Phys. Rev. A 72, 032309 (2005).
46. F. G. S. L. Brandão, "Quantifying entanglement with witness operators," Phys. Rev. A 72, 022310 (2005).
47. For entanglement criteria that are nonlinear in operator expectation values, see, for example, O. Gühne, "Characterizing entanglement via uncertainty relations," Phys. Rev. Lett. 92, 117903 (2004) and references therein.
48. M. Hein, J. Eisert, and H. J. Briegel, "Multiparty entanglement in graph states," Phys. Rev. A 69, 062311 (2004).
49. G. Tóth and O. Gühne, "Detecting genuine multipartite entanglement with two local measurements," Phys. Rev. Lett. 94, 060501 (2005).
50. G. Tóth and O. Güline, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005).
51. O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, "Detection of entanglement with few local measurements," Phys. Rev. A 66, 062305 (2002).
52. B. M. Terhal, "Detecting quantum entanglement," Theor. Comput. Sci. 287, 313-335 (2002).
53. O. Gühne and P. Hyllus, "Investigating three qubit entanglement with local measurements," Int. J. Theor. Phys. 42, 1001-1013 (2003).
54. A. O. Pittenger and M. H. Rubin, "Geometry of entanglement witnesses and local detection of entanglement," Phys. Rev. A 67, 012327 (2003).
55. F. G. S. L. Brandão and R. O. Vianna, "Separable multipartite mixed states: operational asymptotically necessary and sufficient conditions," Phys. Rev. Lett. 93, 220503 (2004).
56. F. G. S. L. Brandão and R. O. Vianna, "Robust semidefinite programming approach to the separability problem," Phys. Rev. A 70, 062309 (2004).
57. J. Eisert, P. Hyllus, O. Gühne, and M. Curty, "Complete hierarchies of efficient approximations to problems in entanglement theory," Phys. Rev. A 70, 062317 (2004).
58. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, "Detecting multipartite entanglement," Phys. Rev. A 71, 032333 (2005).
59. 2≤N(N + 1)/4.
60. E. Solano, Max-Planck-Institute for Quantum Optics, Munich, Germany (personal communication, 2005).
61. G. Tóth and O. Gühne, "Entanglement detection in the stabilizer formalism," Phys. Rev. A 72, 022340 (2005), Appendix C.