Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $τ$ , if its mapped state $ρ$ is EPR steerable, then the state $τ$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $τ$, if its mapped state $ρ$ is EPR steerable, then the state $τ$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.

arXiv:1510.06640Oct 22, 20150 citations

Maximally entangled states and the Bell inequality

Jose Luis Cereceda

arXiv:quant-ph/9812012Physics Letters AMar 1, 19968 citations

Constructing Bell Inequality of Four-Qubit Entangled States

Jianxia Qi, Xin-Wei Zha, Dong Wang

International Journal of Theoretical PhysicsFeb 28, 20120 citations

A new class of Bell-CH inequalities for testing quantum nonlocality

Chen Qian, Yang-Guang Yang, Cong‐Feng Qiao +1 more

Quantum nonlocality can be tested in experiments via the violation of the Bell inequality. We propose novel methods of the rearrangement and linear inequality to prove all the known Bell-CH inequalities of $Imn22$ -type ( $m,n\le5$ ). We also derive a set of new Bell-CH inequalities by using these methods which should be violated in quantum entangled states.Quantum nonlocality can be tested in experiments via the violation of the Bell inequality. We propose novel methods of the rearrangement and linear inequality to prove all the known Bell-CH inequalities of $Imn22$-type ($m,n\le5$). We also derive a set of new Bell-CH inequalities by using these methods which should be violated in quantum entangled states.

Jan 7, 20210 citations

Quantum Entanglement and Bell’s Inequality

Biao Wu

Springer eBooksJan 1, 20231 citation

τ

, if its mapped state

ρ

is EPR steerable, then the state

τ

must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.

Imn22

-type (

m,n\le5

). We also derive a set of new Bell-CH inequalities by using these methods which should be violated in quantum entangled states.