# Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth

 Authors: Yeong-Cherng Liang, Denis Rosset, Jean-Daniel Bancal, Gilles Pütz, Tomer Jack Barnea, Nicolas Gisin Phys. Rev. Lett. 114, 190401 (2015) http://dx.doi.org/10.1103/PhysRevLett.114.190401 We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine k-partite entanglement in an arbitrary n≥k-partite scenario without relying on any assumption about the measurements being performed, or the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as quantum Fisher information. A family of witnesses for genuine k-partite nonlocality applicable to an arbitrary n≥k-partite scenario based on our Bell inequalities is also presented. liang2015a.pdf

# BibTeX Source

@article{PhysRevLett.114.190401,
title = {Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth},
author = {Liang, Yeong-Cherng and Rosset, Denis and Bancal, Jean-Daniel and P\"utz, Gilles and Barnea, Tomer Jack and Gisin, Nicolas},
journal = {Phys. Rev. Lett.},
volume = {114},
issue = {19},
pages = {190401},
numpages = {6},
year = {2015},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.114.190401},
}