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
Journal:Phys. Rev. Lett. 114, 190401 (2015)
DOI:http://dx.doi.org/10.1103/PhysRevLett.114.190401
Abstract: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.
File: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},
  url = {http://link.aps.org/doi/10.1103/PhysRevLett.114.190401},
abstract={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.}
}