Abstract
In device-independent quantum information processing Bell inequalities are not only used as detectors of nonlocality, but also as certificates of relevant quantum properties. In order for these certificates to work, one very often needs Bell inequalities that are maximally violated by specific quantum states. Recently, in Salavrakos et al (2017 Phys. Rev. Lett. 119 040402) a general class of Bell inequalities, with arbitrary numbers of measurements and outcomes, has been designed, which are maximally violated by the maximally entangled states of two quantum systems of arbitrary dimension. In this work, we generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension. We then derive analytically their maximal quantum and nonsignaling values. We also obtain analytically the bound for detecting genuine nonlocality and compute the fully local bound for a few exemplary cases. Moreover, we consider the question of adapting this class of inequalities to partially entangled Greenberger–Horne–Zeilinger-like states for some special cases of low dimension and small number of parties. Through numerical methods, we find classes of inequalities maximally violated by these partially entangled states.
Highlights
Bell inequalities [1] have traditionally been used as witnesses of nonlocality in composite quantum systems, but with the advent of device-independent quantum information processing they gained a completely new role as certificates of relevant quantum properties
Moving to the multipartite case, examples of Bell inequalities for which the realization of the maximal quantum violation is known are: the Mermin Bell inequality [22], the class of Bell inequalities maximally violated by the multiqubit graph states [15], or a class of two-setting Bell inequalities introduced in [16] and tailored to the N-partite Greenberger–Horne– Zeilinger states of arbitrary local dimension å ∣GHZN,dñ =
We provide a general class of multipartite Bell inequalities valid for any number of measurements and outcomes whose maximal quantum violation is attained by the Greenberger–Horne–Zeilinger (GHZ) state of N qudits (1)
Summary
Any further distribution of In device-independent quantum information processing Bell inequalities are used as this work must maintain detectors of nonlocality, and as certificates of relevant quantum properties. In order for these attribution to the author(s) and the title of certificates to work, one very often needs Bell inequalities that are maximally violated by specific the work, journal citation and DOI. We generalize these results to the multipartite scenario and obtain a general class of Bell inequalities maximally violated by the Greenberger–Horne–Zeilinger states of any number of parties and any local dimension.
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