Violations of Bell inequalities from random pure states
Abstract
We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalised version of the CGLMP inequality, which concerns Bell experiments of two parties, two measurement options and N outcomes and analyse their expected quantum violations from random pure states for varying N, assuming the conjectured optimal measurement operators. It is seen that for small N the Bell inequality is not violated on average, while for larger N it is. Both ensembles of unstructured as well as structured random pure states are considered. Using techniques from random matrix theory this is obtained analytically for small and large N and numerically for intermediate N. The results show a beautiful interplay of different aspects of random matrix theory, ranging from the Marchenko-Pastur distribution and fixed-trace ensembles to the O(n) model.
Keywords
Cite
@article{arxiv.1407.8233,
title = {Violations of Bell inequalities from random pure states},
author = {Max R. Atkin and Stefan Zohren},
journal= {arXiv preprint arXiv:1407.8233},
year = {2015}
}
Comments
7 pages, 3 figures, v2: new results included on structured ensembles, previous results unchanged, expanded introductory chapter and restructuring through appendices