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DOI: 10.4230/LIPIcs.TQC.2016.5
URN: urn:nbn:de:0030-drops-66867
URL: http://drops.dagstuhl.de/opus/volltexte/2016/6686/
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Laplante, Sophie ; Laurière, Mathieu ; Nolin, Alexandre ; Roland, Jérémie ; Senno, Gabriel

Robust Bell Inequalities from Communication Complexity

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Abstract

The question of how large Bell inequality violations can be, for quantum distributions, has been the object of much work in the past several years. We say a Bell inequality is normalized if its absolute value does not exceed 1 for any classical (i.e. local) distribution. Upper and (almost) tight lower bounds have been given in terms of number of outputs of the distribution, number of inputs, and the dimension of the shared quantum states. In this work, we revisit normalized Bell inequalities together with another family: inefficiency-resistant Bell inequalities. To be inefficiency-resistant, the Bell value must not exceed 1 for any local distribution, including those that can abort. Both these families of Bell inequalities are closely related to communication complexity lower bounds. We show how to derive large violations from any gap between classical and quantum communication complexity, provided the lower bound on classical communication is proven using these lower bounds. This leads to inefficiency-resistant violations that can be exponential in the size of the inputs. Finally, we study resistance to noise and inefficiency for these Bell inequalities.

BibTeX - Entry

@InProceedings{laplante_et_al:LIPIcs:2016:6686,
  author =	{Sophie Laplante and Mathieu Lauri{\`e}re and Alexandre Nolin and J{\'e}r{\'e}mie Roland and Gabriel Senno},
  title =	{{Robust Bell Inequalities from Communication Complexity}},
  booktitle =	{11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-019-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{61},
  editor =	{Anne Broadbent},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6686},
  URN =		{urn:nbn:de:0030-drops-66867},
  doi =		{10.4230/LIPIcs.TQC.2016.5},
  annote =	{Keywords: Communication complexity, Bell inequalities, nonlocality, detector efficiency}
}

Keywords: Communication complexity, Bell inequalities, nonlocality, detector efficiency
Seminar: 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)
Issue Date: 2016
Date of publication: 13.09.2016


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