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

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

Entanglement without hidden nonlocality

Flavien Hirsch, Marco Túlio Quintino, Joseph Bowles +2 more

We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.

arXiv:1606.02215New Journal of PhysicsNov 9, 201653 citations

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.