Random and free observables saturate the Tsirelson bound for CHSH inequality
Abstract
Maximal violation of the CHSHBell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit nearmaximal violations of the CHSHBell 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 infinitedimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the finegrained uncertainty of a sequence of free or random observables, and use this to construct a steering inequality with a large violation.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 DOI:
 10.48550/arXiv.1512.00223
 arXiv:
 arXiv:1512.00223
 Bibcode:
 2015arXiv151200223Y
 Keywords:

 Quantum Physics
 EPrint:
 Phys. Rev. A 95, 032101 (2017)