Abstract
We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented.
Highlights
We study the nonlocality of arbitrary dimensional bipartite quantum states
This bound gives the necessary condition that a two-qubit state admits no local hidden variable models
In the paper we study the nonlocality of arbitrary two-qubit states and present an analytical and computable lower bound of the quantity Q by computing the maximal violation of a set of multi-setting Bell inequalities
Summary
Ming Li1,5, Tinggui Zhang[2,5], Bobo Hua[3,5], Shao-Ming Fei4,5 & Xianqing Li-Jost[2,5] received: 12 May 2015 accepted: 23 July 2015 Published: 25 August 2015. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. A bipartite quantum state may violates some Bell inequalities such that the local measurement outcomes can not be modeled by classical random distributions over probability spaces. To show that a quantum state admits no LHV models, it is sufficient to show that it violates a Bell inequality[15,16].
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