Random and free observables saturate the Tsirelson bound for CHSH inequality
Quantum Physics
2017-03-08 v3
Abstract
Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables" which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation.
Keywords
Cite
@article{arxiv.1512.00223,
title = {Random and free observables saturate the Tsirelson bound for CHSH inequality},
author = {Z. Yin and A. W. Harrow and M. Horodecki and M. Marciniak and A. Rutkowski},
journal= {arXiv preprint arXiv:1512.00223},
year = {2017}
}