Exploring Bell inequalities for the device-independent certification of multipartite entanglement depth

Abstract

Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement depth) present in certain well-known multipartite quantum states, including the generalized Greenberger-Horne-Zeilinger (GHZ) states with unbalanced weights, the higher-dimensional generalizations of balanced GHZ states, and the $W$ states. As a by-product of our investigations, we have found that, in contrast with well-established results, provided trivial qubit measurements are allowed, full-correlation Bell inequalities can also be used to demonstrate the nonlocality of weakly entangled unbalanced-weight GHZ states. Besides, we also demonstrate how two-setting, two-outcome Bell inequalities can be constructed, based on the so-called GHZ paradox, to witness the entanglement depth of various graph states, including the ring graph states, the fully connected graph states, and some linear graph states, etc.

arXiv commentEssentially published version, but with the typo in Eq. (C2) corrected

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• Semidefinite programming relaxations for quantum correlations
• Device-independent witnesses of entanglement depth from two-body correlators
• k-stretchability of entanglement, and the duality of k-separability and k-producibility
• Optimization of device-independent witnesses of entanglement depth from two-body correlators
• Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads
• Bell inequalities for nonlocality depth
• Quantifying multipartite quantum states by ($k+1$)-partite entanglement measures
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Minimal scenario facet Bell inequalities for multi-qubit states
• Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Complete $k$-partite entanglement measure