Theory of genuine tripartite nonlocality of Gaussian states

Physical Review Letters

Volumn 112, Issue 1, 2014, Pages

  Adesso, Gerardo ^a   Piano, Samanta ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS VARIABLE SYSTEM; EXPERIMENTAL VERIFICATION; GAUSSIAN STATE; NONLOCALITIES; SIMPLIFIED PROCEDURE; TRIPARTITE ENTANGLEMENT; UPPER AND LOWER BOUNDS; WIGNER FUNCTIONS;

QUANTUM ENTANGLEMENT;

GAUSSIAN DISTRIBUTION;

EID: 84892404836     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.010401     Document Type: Article

References (48)

1. G. Adesso and D. Girolami, Nat. Photonics 6, 579 (2012). NPAHBY 1749-4885 10.1038/nphoton.2012.214
2. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935). PHRVAO 0031-899X 10.1103/PhysRev.47.777
3. J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964); PHYSGM 1943-2879 3b J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, England, 1987).
4. J. Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Rev. Lett. 23, 880 (1969). PRLTAO 0031-9007 10.1103/PhysRevLett.23.880
5. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, arXiv:1303.2849.
6. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.865
7. E. Schrödinger, Naturwissenschaften 23, 812 (1935). NATWAY 0028-1042 10.1007/BF01491892
8. R. F. Werner, Phys. Rev. A 40, 4277 (1989). PLRAAN 0556-2791 10.1103/PhysRevA.40.4277
9. R. Gallego, L. E. Würflinger, A. Acín, and M. Navascués, Phys. Rev. Lett. 109, 070401 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.070401
10. J. Barrett, L. Hardy, and A. Kent, Phys. Rev. Lett. 95, 010503 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.010503 10b A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Phys. Rev. Lett. 98, 230501 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.230501 10c L. Masanes, Phys. Rev. Lett. 102, 140501 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.102.140501 10d L. Masanes, S. Pironio, and A. Acín, Nat. Commun. 2, 238 (2011). NCAOBW 2041-1723 10.1038/ncomms1244 (Pubitemid 41506418)
11. N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990); PRLTAO 0031-9007 10.1103/PhysRevLett.65.1838 11b D. N. Klyshko, Phys. Lett. A 172, 399 (1993). PYLAAG 0375-9601 10.1016/0375-9601(93)90228-R
12. G. Svetlichny, Phys. Rev. D 35, 3066 (1987). PRVDAQ 0556-2821 10.1103/PhysRevD.35.3066
13. J.-D. Bancal, N. Brunner, N. Gisin, and Y.-C. Liang, Phys. Rev. Lett. 106, 020405 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.020405
14. S. Ghose, N. Sinclair, S. Debnath, P. Rungta, and R. Stock, Phys. Rev. Lett. 102, 250404 (2009); PRLTAO 0031-9007 10.1103/PhysRevLett.102.250404 14b A. Ajoy and P. Rungta, Phys. Rev. A 81, 052334 (2010). PLRAAN 1050-2947 10.1103/PhysRevA.81.052334
15. J. Lavoie, R. Kaltenbaek, and K. J. Resch, New J. Phys. 11, 073051 (2009). NJOPFM 1367-2630 10.1088/1367-2630/11/7/073051
16. M. Seevinck and G. Svetlichny, Phys. Rev. Lett. 89 060401 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.060401 16b D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, Phys. Rev. Lett. 88, 170405 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.88.170405 16c P. Mitchell, S. Popescu, and D. Roberts, Phys. Rev. A 70, 060101 (2004); PLRAAN 1050-2947 10.1103/PhysRevA.70.060101 16d N. S. Jones, N. Linden, and S. Massar, Phys. Rev. A 71, 042329 (2005); PLRAAN 1050-2947 10.1103/PhysRevA.71.042329 16e J.-D. Bancal, C. Branciard, N. Gisin, and S. Pironio, Phys. Rev. Lett.. 103, 090503 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.090503
17. J.-D. Bancal, J. Barrett, N. Gisin, and S. Pironio, Phys. Rev. A 88, 014102 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.88.014102
18. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000). PLRAAN 1050-2947 10.1103/PhysRevA.61.052306
19. H. Nha and H. J. Carmichael, Phys. Rev. Lett. 93, 020401 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.93.020401 19b R. García-Patrón, J. Fiurášek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and P. Grangier, Phys. Rev. Lett. 93, 130409 (2004); PRLTAO 0031-9007 10.1103/PhysRevLett.93.130409 19c R. García-Patrón, J. Fiurášek, and N. J. Cerf, Phys. Rev. A 71, 022105 (2005). PLRAAN 1050-2947 10.1103/PhysRevA.71.022105
20. K. Banaszek and K. Wodkiewicz, Phys. Rev. Lett. 76, 4344 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.4344
21. H. Jeong, W. Son, M. S. Kim, D. Ahn, and C. Brukner, Phys. Rev. A 67, 012106 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.67.012106
22. P. van Loock and S. L. Braunstein, Phys. Rev. A 63, 022106 (2001). PLRAAN 1050-2947 10.1103/PhysRevA.63.022106
23. Z. B. Chen, J. W. Pan, G. Hou, and Y. D. Zhang, Phys. Rev. Lett. 88, 040406 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.88.040406
24. A. Ferraro and M. G. A. Paris, J. Opt. B 7, 174 (2005). JOBOFD 1464-4266 10.1088/1464-4266/7/6/003 (Pubitemid 40761095)
25. A. Acín, N. J. Cerf, A. Ferraro, and J. Niset, Phys. Rev. A 79, 012112 (2009). PLRAAN 1050-2947 10.1103/PhysRevA.79.012112
26. J. Li, T. Fogarty, C. Cormick, J. Goold, T. Busch, and M. Paternostro, Phys. Rev. A 84, 022321 (2011). PLRAAN 1050-2947 10.1103/PhysRevA.84.022321
27. S. W. Lee, M. Paternostro, J. Lee, and H. Jeong, Phys. Rev. A 87, 022123 (2013). PLRAAN 1050-2947 10.1103/PhysRevA.87.022123
28. S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005). RMPHAT 0034-6861 10.1103/RevModPhys.77.513 (Pubitemid 41491330)
29. C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012). RMPHAT 0034-6861 10.1103/RevModPhys.84.621
30. Quantum Information with Continuous Variables of Atoms and Light, edited by N. Cerf, G. Leuchs, and E. S. Polzik (Imperial College Press, London, 2007).
31. G. Adesso and F. Illuminati, J. Phys. A 40, 7821 (2007). JPAMB5 1751-8113 10.1088/1751-8113/40/28/S01
32. J. Fiurášek, Phys. Rev. Lett. 89, 137904 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.137904 32b J. Eisert, S. Scheel, and M. B. Plenio, Phys. Rev. Lett. 89, 137903 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.137903 32c G. Giedke and J. I. Cirac, Phys. Rev. A 66, 032316 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.66.032316
33. G. Adesso, D. Girolami, and A. Serafini, Phys. Rev. Lett. 109, 190502 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.190502
34. A. Mari, K. Kieling, B. M. Nielsen, E. S. Polzik, and J. Eisert, Phys. Rev. Lett. 106, 010403 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.010403
35. A. Mari and J. Eisert, Phys. Rev. Lett. 109, 230503 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.230503
36. S. Piano and G. Adesso, Entropy 15, 1875 (2013). ENTRFG 1099-4300 10.3390/e15051875
37. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A 73, 032345 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.73.032345
38. G. Adesso, A. Serafini, and F. Illuminati, New J. Phys. 9, 60 (2007). NJOPFM 1367-2630 10.1088/1367-2630/9/3/060 (Pubitemid 46453744)
39. G. Adesso and F. Illuminati, New J. Phys. 8, 15 (2006). NJOPFM 1367-2630 10.1088/1367-2630/8/1/015
40. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Phys. Rev. A 64, 052303 (2001). PLRAAN 1050-2947 10.1103/PhysRevA.64.052303
41. P. van Loock and S. L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.3482 41b G. Adesso and F. Illuminati, Phys. Rev. Lett. 95, 150503 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95. 150503
42. H. Yonezawa, T. Aoki, and A. Furusawa, Nature (London) 431, 430 (2004). NATUAS 0028-0836 10.1038/nature02858 (Pubitemid 39329577)
43. R. Neigovzen, C. Rodó, G. Adesso, and A. Sanpera, Phys. Rev. A 77, 062307 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.77.062307
44. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, Phys. Rev. Lett. 92, 177903 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.177903
45. Precisely, there are 185 × 2 6 inequalities, as for each one there are two possible relabelings for the outcomes of each local measurement. The #185 N S 2 inequality facet in [17] is the conventional Svetlichny one [12]. Notice that each of those inequalities can be violated up to a different extent, so the quantitative amounts of their violation are incomparable. Some inequalities such as #1 can never be violated. Others can be violated only for certain types of fully inseparable states, or certain ranges of local CM parameters in the case of Gaussian states.
46. N. Gisin, Phys. Lett. A 154, 201 (1991). PYLAAG 0375-9601 10.1016/0375-9601(91)90805-I
47. A. S. Coelho, F. A. S. Barbosa, K. N. Cassemiro, A. S. Villar, M. Martinelli, and P. Nussenzveig, Science 326, 823 (2009). SCIEAS 0036-8075 10.1126/science.1178683
48. H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Rev. Mod. Phys. 85, 553 (2013). RMPHAT 0034-6861 10.1103/RevModPhys.85.553