Logical Families of Nonlocal Boxes - TEL - Département Télécommunications Access content directly
Conference Papers Year : 2015

Logical Families of Nonlocal Boxes


In this paper, we will study the behavior of nonlocal boxes and non-signaling boxes by calculating a Bell Inequalities (BI) for all possible logical combinations of inputs and outputs. We have considered the case of equal number n of inputs and outputs, first for n = 2 using the CHSH BI and then generalized to the case n = 3 using the Svetlichny BI. n = 2 corresponds to 256 cases and increases exponentially for n = 3 (256x 256 = 65536 cases). We thus developped a computer program for processing the different cases by calculating the inequalities and also testing non-signaling in a systematic way. Maximal Bell parameter of 4 is obtained for the no-signaling family of 16 nonlocal boxes the PR Box being part of this family. Another family of 32 nonlocal boxes (green cases) is signaling and giving a BI violation 10/3 > 2sqrt(2)> 2, exceeding the quantum limit. The three-party correlation logical boxes give 65536 combinations of logical functions. Calculation (computer) of the Svetlichny leads to nonlocality for six different values.
Fichier principal
Vignette du fichier
GDR-IQFA_TemplateNLBox_final.pdf (140.3 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01261836 , version 1 (25-01-2016)
hal-01261836 , version 2 (13-02-2018)


  • HAL Id : hal-01261836 , version 1


Zeno Toffano, Cassandre Chatard, Kaicheng Ding, Alice Portalier, Gregoire Vilde. Logical Families of Nonlocal Boxes. Colloque IQFA 2015 , GdR IQFA, Nov 2015, Palaiseau, France. ⟨hal-01261836v1⟩


149 View
140 Download


Gmail Facebook Twitter LinkedIn More