Optimisation of Bell inequalities with invariant Tsirelson bound
Abstract
We consider a subclass of bipartite CHSH-type Bell inequalities. We investigate operations, which leave their Tsirelson bound invariant, but change their classical bound. The optimal observables are unaffected except for a relative rotation of the two laboratories. We illustrate the utility of these operations by giving explicit examples: We prove that for a fixed quantum state and fixed measurement setup except for a relative rotation of the two laboratories, there is a Bell inequality that is maximally violated for this rotation, and we optimise some Bell inequalities with respect to the maximal violation. Finally we optimise the qutrit to qubit ratio of some dimension witnessing Bell inequalities.
Keywords
Cite
@article{arxiv.1402.0378,
title = {Optimisation of Bell inequalities with invariant Tsirelson bound},
author = {Michael Epping and Hermann Kampermann and Dagmar Bruß},
journal= {arXiv preprint arXiv:1402.0378},
year = {2014}
}
Comments
12 pages, 2 figures; contribution to special issue of JPA: 50 years of Bell's theorem