Publication: Unbounded Bell violations for quantum genuine multipartite non-locality
Loading...
Official URL
Full text at PDC
Publication Date
2020
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP
Citations
Exportar
Abstract
The violations of Bell inequalities by measurements on quantum states give rise to the phenomenon of quantum non-locality and express the advantage of using quantum resources over classical ones for certain information-theoretic tasks. The relative degree of quantum violations has been well studied in the bipartite scenario and in the multipartite scenario with respect to fully local behaviours. However, the multipartite setting entails a more complex classification in which different notions on non-locality can be established. In particular, genuine multipartite non-local distributions apprehend truly multipartite effects, given that these behaviours cannot be reproduced by bilocal models that allow correlations among strict subsets of the parties beyond a local common cause. We show here that, while in the so-called correlation scenario the relative violation of bilocal Bell inequalities by quantum resources is bounded, i.e. it does not grow arbitrarily with the number of inputs, it turns out to be unbounded in the general case. We identify Bell functionals that take the form of non-local games for which the ratio of the quantum and bilocal values grows unboundedly as a function of the number of inputs and outputs.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[1] Acín A, Brunner N, Gisin N, Massar S, Pironio S and Scarani V 2007 Phys. Rev. Lett. 98 230501
[2] Almeida M L, Cavalcanti D, Scarani V and Acín A 2010 Phys. Rev. A 81 052111
[3] Bancal J-D, Barrett J, Gisin N and Pironio S 2013 Phys. Rev. A 88 014102
[4] Bancal J-D, Branciard C, Gisin N and Pironio S 2009 Phys. Rev. Lett. 103 090503
[5] Bell J S 1964 Physics 1 195
[6] Briet J and Vidick T 2013 Commun. Math. Phys. 321 181–207
[7] Brunner N, Cavalcanti D, Pironio S, Scarani V and Wehner S 2014 Rev. Mod. Phys. 86 419
[8] Buhrman H, Regev O, Scarpa G and de Wolf R 2012 Theory Comput. 8 623–45
[9] Cleve R and Buhrman H 1997 Phys. Rev. A 56 1201
[10] Cleve R, Hoyer P, Toner B and Watrous J 2004 Proc. 19th IEEE CCC pp 236–49
[11] Colbeck R and Renner R 2012 Nat. Phys. 8 450
[12] Collins D, Gisin N, Popescu S, Roberts D and Scarani V 2002 Phys. Rev. Lett. 88 170405
[13] Curchod F J, Almeida M L and Acín A 2019 New J. Phys. 21 023016
[14] Degorre J,Kaplan M, Laplante S and Roland J 2009 Mathematical Foundations of Computer Science MFCS 2009 (Lecture Notes in Computer Science vol 5734) ed R Královic and D Niwinski (Berlin, Heidelberg: Springer) pp 270–81
[15] Ekert A K 1991 Phys. Rev. Lett. 67 661
[16] Gallego R, Würflinger L E, Acín A and Navascués M 2012 Phys. Rev. Lett. 109 070401
[17] Gallego R, Masanes L, de la Torre G, Dhara C, Aolita L and Acín A 2013 Nat. Commun. 4 2654
[18] Jones N S, Linden N and Massar S 2005 Phys. Rev. A 71 042329
[19] Junge M and Palazuelos C 2011 Commun. Math. Phys. 306 695–746
[20] Junge M, Palazuelos C, Pérez-García D, Villanueva I and Wolf M M 2010 Commun. Math. Phys. 300 715–39
[21] Junge M, Palazuelos C, Pérez-García D, Villanueva I and Wolf M M 2010 Phys. Rev. Lett. 104 170405
[22] Khot S and Vishnoi N 2005 Proc. 46th IEEE FOCS pp 53–62
[23] Lami L, Palazuelos C and Winter A 2018 Commun. Math. Phys. 361 661–708
[24] Lancien C and Winter A 2016 Chicago J. Theor. Comput. Sci. 2016 11
[25] Palazuelos C 2018 Found. Phys. 48 857–85
[26] Palazuelos C and Vidick T 2016 J. Math. Phys. 57 015220
[27] Pérez-García D, Wolf M M, Palazuelos C, Villanueva I and Junge M 2008 Commun. Math. Phys. 279 455–86
[28] Pironio S et al 2010 Nature 464 1021
[29] Popescu S and Rohrlich D 1994 Found. Phys. 24 379
[30] Seevinck M and Svetlichny G 2002 Phys. Rev. Lett. 89 060401
[31] Svetlichny G 1987 Phys. Rev. D 35 3066
[32] Tsirelson B S 1993 Hadronic J. Supp. 8 329–45
[33] Vazirani U and Vidick T 2014 Phys. Rev. Lett. 113 140501
[34] Weisstein E W 2020 Mathworld–a Wolfram web resource
http://mathworld.wolfram.com/HadamardMatrix.html