The question of the possible existence of hidden variables is re-examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every other one. It is further shown that this property is in contradiction with empirical facts. The theorem which leads to this conclusion is a strengthening of the theorem of von Neumann on the same subject. The question is raised whether there exist perhaps quantum mechanical systems which admit approximate dispersion-free states.The question of the possible existence of hidden variables is re-examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every other one. It is further shown that this property is in contradiction with empirical facts. The theorem which leads to this conclusion is a strengthening of the theorem of von Neumann on the same subject. The question is raised whether there exist perhaps quantum mechanical systems which admit approximate dispersion-free states.

Dec 15, 196399 citations

Algebraic constraints on hidden variables

Arthur I. Fine, Paul Teller

Foundations of PhysicsAug 1, 197825 citations

Remarks on the Hypothesis of Hidden Variables

F. Pollini

Springer eBooksJan 1, 19880 citations

Quantum Discord, CHSH Inequality and Hidden Variables -- Critical reassessment of hidden-variables models

Kazuo Fujikawa

Hidden-variables models are critically reassessed. It is first examined if the quantum discord is classically described by the hidden-variable model of Bell in the Hilbert space with $d=2$ . The criterion of vanishing quantum discord is related to the notion of reduction and, surprisingly, the hidden-variable model in $d=2$ , which has been believed to be consistent so far, is in fact inconsistent and excluded by the analysis of conditional measurement and reduction. The description of the full contents of quantum discord by the deterministic hidden-variables models is not possible. We also re-examine CHSH inequality. It is shown that the well-known prediction of CHSH inequality $|B|\leq 2$ for the CHSH operator $B$ introduced by Cirel'son is not unique. This non-uniqueness arises from the failure of linearity condition in the non-contextual hidden-variables model in $d=4$ used by Bell and CHSH, in agreement with Gleason's theorem which excludes $d=4$ non-contextual hidden-variables models. If one imposes the linearity condition, their model is converted to a factored product of two $d=2$ models which describes quantum mechanical separable states. The CHSH inequality thus does not test the hidden-variables model in $d=4$ . This observation is consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to dispersion-free representations. As for hidden-variables models, there exist no viable local non-contextual models in any dimensions.Hidden-variables models are critically reassessed. It is first examined if the quantum discord is classically described by the hidden-variable model of Bell in the Hilbert space with $d=2$. The criterion of vanishing quantum discord is related to the notion of reduction and, surprisingly, the hidden-variable model in $d=2$, which has been believed to be consistent so far, is in fact inconsistent and excluded by the analysis of conditional measurement and reduction. The description of the full contents of quantum discord by the deterministic hidden-variables models is not possible. We also re-examine CHSH inequality. It is shown that the well-known prediction of CHSH inequality $|B|\leq 2$ for the CHSH operator $B$ introduced by Cirel'son is not unique. This non-uniqueness arises from the failure of linearity condition in the non-contextual hidden-variables model in $d=4$ used by Bell and CHSH, in agreement with Gleason's theorem which excludes $d=4$ non-contextual hidden-variables models. If one imposes the linearity condition, their model is converted to a factored product of two $d=2$ models which describes quantum mechanical separable states. The CHSH inequality thus does not test the hidden-variables model in $d=4$. This observation is consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to dispersion-free representations. As for hidden-variables models, there exist no viable local non-contextual models in any dimensions.

arXiv:1302.0916Feb 5, 20130 citations

Approximate Hidden Variables

M. Zisis

Foundations of PhysicsJul 1, 20003 citations

A Bell-type theorem without hidden variables

Henry Pierce Stapp

It is shown that no theory that satisfies certain premises can exclude faster-than-light influences. The premises include neither the existence of hidden variables nor counterfactual definiteness, nor any premise that effectively entails the general existence of outcomes of unperformed local measurements. All the premises are compatible with Copenhagen philosophy and the principles and predictions of relativistic quantum field theory. The present proof is contrasted with an earlier one with the same objective.It is shown that no theory that satisfies certain premises can exclude faster-than-light influences. The premises include neither the existence of hidden variables nor counterfactual definiteness, nor any premise that effectively entails the general existence of outcomes of unperformed local measurements. All the premises are compatible with Copenhagen philosophy and the principles and predictions of relativistic quantum field theory. The present proof is contrasted with an earlier one with the same objective.

arXiv:quant-ph/0205096American Journal of PhysicsDec 12, 200331 citations

Hidden-variables models are critically reassessed. It is first examined if the quantum discord is classically described by the hidden-variable model of Bell in the Hilbert space with

d=2

. The criterion of vanishing quantum discord is related to the notion of reduction and, surprisingly, the hidden-variable model in

d=2

, which has been believed to be consistent so far, is in fact inconsistent and excluded by the analysis of conditional measurement and reduction. The description of the full contents of quantum discord by the deterministic hidden-variables models is not possible. We also re-examine CHSH inequality. It is shown that the well-known prediction of CHSH inequality

|B|\leq 2

for the CHSH operator

B

introduced by Cirel'son is not unique. This non-uniqueness arises from the failure of linearity condition in the non-contextual hidden-variables model in

d=4

used by Bell and CHSH, in agreement with Gleason's theorem which excludes

d=4

non-contextual hidden-variables models. If one imposes the linearity condition, their model is converted to a factored product of two

d=2

models which describes quantum mechanical separable states. The CHSH inequality thus does not test the hidden-variables model in

d=4

. This observation is consistent with an application of the CHSH inequality to quantum cryptography by Ekert, which is based on mixed separable states without referring to dispersion-free representations. As for hidden-variables models, there exist no viable local non-contextual models in any dimensions.