John Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions. 1. Introduction2. The EPR-Bohm experiment3. Local causality4. Bell's inequality from separate common causes4.1A weak screening-off principle4.2Perfect correlation and ‘determinism’4.3A minimal theory for spins4.4No conspiracy5. DiscussionJohn Bell showed that a big class of local hidden-variable models stands in conflict with quantum mechanics and experiment. Recently, there were suggestions that empirically adequate hidden-variable models might exist which presuppose a weaker notion of local causality. We will show that a Bell-type inequality can be derived also from these weaker assumptions. 1. Introduction2. The EPR-Bohm experiment3. Local causality4. Bell's inequality from separate common causes4.1A weak screening-off principle4.2Perfect correlation and ‘determinism’4.3A minimal theory for spins4.4No conspiracy5. Discussion

arXiv:quant-ph/0312176The British Journal for the Philosophy of ScienceOct 19, 200564 citations

The Irrelevance of the Bell Inequality

Thomas A. Brody

Springer eBooksJan 1, 19930 citations

Separability inequalities on N-qudit correlations exponentially stronger than local reality inequalities

Shasanka Mohan Roy

I derive separability inequalities for Bell correlations of observables in arbitrary pure or mixed $N$ Qudit states in $D^N$ -dimensional state space. I find states (a continuum of states if $D>3$ ) including maximally entangled states which violate these inequalities by a factor $2^{N-1}$ ; local reality Bell inequalities are much weaker, their maximum violation being by a factor $2^{(N-1)/2}$ . The separability inequalities allow tests of entanglement of unknown states using only the measured correlations .I derive separability inequalities for Bell correlations of observables in arbitrary pure or mixed $N$ Qudit states in $D^N$-dimensional state space. I find states (a continuum of states if $D>3$) including maximally entangled states which violate these inequalities by a factor $2^{N-1}$ ; local reality Bell inequalities are much weaker, their maximum violation being by a factor $2^{(N-1)/2}$. The separability inequalities allow tests of entanglement of unknown states using only the measured correlations .

arXiv:2001.11687Jan 31, 20200 citations

A stronger form of Bell’s inequality

F. Selleri

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoApr 1, 197211 citations

Counter-Factual Meaningfulness and the Bell and CHSH Inequalities

Travis Norsen

We discuss the role of counter-factual meaningfulness (a weaker cousin of "counter-factual definiteness") as a premise in the derivation of the Bell and CHSH inequalities. The basic question motivating the discussion is this: can the CHSH inequality, unlike the original Bell inequality, be derived without making a hidden-variables (or equivalent counter-factual definiteness) assumption? We answer, somewhat tentatively, in the negative, and suggest that an appropriately-modified version of the EPR argument is needed to rigorously establish that the empirical violation of Bell-type inequalities can only be blamed on the failure, in nature, of local causality.We discuss the role of counter-factual meaningfulness (a weaker cousin of "counter-factual definiteness") as a premise in the derivation of the Bell and CHSH inequalities. The basic question motivating the discussion is this: can the CHSH inequality, unlike the original Bell inequality, be derived without making a hidden-variables (or equivalent counter-factual definiteness) assumption? We answer, somewhat tentatively, in the negative, and suggest that an appropriately-modified version of the EPR argument is needed to rigorously establish that the empirical violation of Bell-type inequalities can only be blamed on the failure, in nature, of local causality.

arXiv:quant-ph/0606084Jun 9, 20062 citations

I derive separability inequalities for Bell correlations of observables in arbitrary pure or mixed

N

Qudit states in

D^N

-dimensional state space. I find states (a continuum of states if

D>3

) including maximally entangled states which violate these inequalities by a factor

2^{N-1}

; local reality Bell inequalities are much weaker, their maximum violation being by a factor

2^{(N-1)/2}

. The separability inequalities allow tests of entanglement of unknown states using only the measured correlations .