Eur. Phys. J. D (2016) 70: 205
https://doi.org/10.1140/epjd/e2016-60577-y

Regular Article

Relations among non-chordal compatibility graphs, imperfect exclusivity graphs and quantum correlations^*

Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing, 100084, P.R. China

^a e-mail: zwei@mail.tsinghua.edu.cn

Received: 13 October 2015
Received in final form: 31 August 2016
Published online: 13 October 2016

Abstract

The relations among non-chordal compatibility graphs, imperfect exclusivity graphs and quantum correlations are investigated in the scenario where the compatibility relations and the events are fixed. In this scenario, we prove that the non-chordal compatibility graph is a sufficient condition for exhibiting quantum correlations and the imperfect exclusivity graph is an insufficient condition for exhibiting quantum correlations. The result provides a convenient tool to determine whether an observable set can distinguish the quantum from classical correlations.