A Bell inequality violation allowed by the two-mode squeezed state, whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables that cannot be interpreted via a local hidden variable theory. Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky, and Rosen) state will not allow violation of Bell's inequality, in conjunction with its Wigner representative being nonnegative. It is argued that Bell's theorem disallowing the violation of Bell's inequality within a local hidden-variable theory depends on the dynamical variables having a definite value---assigned by the local hidden variables---even when they cannot be simultaneously measured. The analysis leads us to conclude that Bell's inequality violation is to be associated with endowing these definite values to the dynamical variables, and not with their locality attributes.A Bell inequality violation allowed by the two-mode squeezed state, whose Wigner function is nonnegative, is shown to hold only for correlations among dynamical variables that cannot be interpreted via a local hidden variable theory. Explicit calculations and interpretation are given for Bell's suggestion that the EPR (Einstein, Podolsky, and Rosen) state will not allow violation of Bell's inequality, in conjunction with its Wigner representative being nonnegative. It is argued that Bell's theorem disallowing the violation of Bell's inequality within a local hidden-variable theory depends on the dynamical variables having a definite value---assigned by the local hidden variables---even when they cannot be simultaneously measured. The analysis leads us to conclude that Bell's inequality violation is to be associated with endowing these definite values to the dynamical variables, and not with their locality attributes.

arXiv:quant-ph/0405100Physical Review AFeb 10, 200559 citations

Experimental violation of a Bell's inequality with efficient detection

M. A. Rowe, D. Kielpinski, V. Meyer +4 more

NatureFeb 15, 20011,055 citations

Bell's Theorem: a new Derivation that Preserves Heisenberg and Locality

M. R. Clover

By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time dependent, non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty Principle) can satisfy this new bound while exceeding Bell's limit. Unconditional nonlocality is only expected to occur with Bell parameters between $2\sqrt{2}$ and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.By implicitly assuming that all measurements occur simultaneously, Bell's Theorem only applied to local theories that violated Heisenberg's Uncertainty Principle. By explicitly introducing time into our derivation of Bell's theorem, an extra term related to the time-ordering of actual measurements is found to augment (i.e. weaken) the upper bound of the inequality. Since the same locality assumptions hold for this rederivation as for the original, we conclude that only {\em classical} measurement-order independent local hidden variable theories are constrained by Bell's inequality; time dependent, non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty Principle) can satisfy this new bound while exceeding Bell's limit. Unconditional nonlocality is only expected to occur with Bell parameters between $2\sqrt{2}$ and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.

arXiv:quant-ph/0409058Sep 10, 20048 citations

Experimental Tests of Bell’s Inequalities

Alain Aspect, Philippe Grangier

NATO ASI series. Series B : PhysicsJan 1, 19952 citations

The EPR-B Paradox Resolution. Bell inequalities revisited.

Jaykov Foukzon, Менькова Елена Романовна, Alexander A Potapov

Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.

Journal of Physics Conference SeriesNov 1, 20190 citations

2\sqrt{2}

and 4. This weakening of Bell's inequality is seen for the quantum Bell operator (squared) as an extra term involving the commutators of {\em local} measurement operators. We note that a factorizable second-quantized wavefunction can reproduce experimental measurements; because such wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have another indication that violation of {\em Bell's} inequality does not require an acceptance of non-locality.