title: Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth.
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.
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.|Department of Physics, National Cheng Kung University, Tainan 701, Taiwan.
authors.forename: Yeong-Cherng
authors.initials: YC
authors.lastname: Liang
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Denis
authors.initials: D
authors.lastname: Rosset
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
authors.forename: Jean-Daniel
authors.initials: JD
authors.lastname: Bancal
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Gilles
authors.initials: G
authors.lastname: Pütz
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Tomer Jack
authors.initials: TJ
authors.lastname: Barnea
authors.affiliation: Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Gisin