Family of bell-like inequalities as device-independent witnesses for entanglement depth

Yeong Cherng Liang, Denis Rosset, Jean Daniel Bancal, Gilles Pütz, Tomer Jack Barnea, Nicolas Gisin

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


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.

Original languageEnglish
Article number190401
JournalPhysical review letters
Issue number19
Publication statusPublished - 2015 May 12

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)


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