Several authors have recently claimed that Bell's inequalities (BI) do not apply to certain types of generalized local hidden variables (HV) models. These claims are rejected, by means of a proof of BI valid for a very broad class of local HV models (deterministic or stochastic, with or without memory, time dependent or time independent, setting dependent or setting independent, and even allowing classical communication between the wings of the experiment). The precise meaning of the locality requirement is clarified during the proof. The exact roles of the two assumptions that amount to Bell's locality (parameter independence and outcome independence) are explicitly shown, using each one of them in a different step of the proof. using each one of them in a different step of the proof.Several authors have recently claimed that Bell's inequalities (BI) do not apply to certain types of generalized local hidden variables (HV) models. These claims are rejected, by means of a proof of BI valid for a very broad class of local HV models (deterministic or stochastic, with or without memory, time dependent or time independent, setting dependent or setting independent, and even allowing classical communication between the wings of the experiment). The precise meaning of the locality requirement is clarified during the proof. The exact roles of the two assumptions that amount to Bell's locality (parameter independence and outcome independence) are explicitly shown, using each one of them in a different step of the proof. using each one of them in a different step of the proof.

arXiv:quant-ph/0211188Nov 28, 20020 citations

Generalized Bell-inequality experiments and computation

Matty J. Hoban, Joel J. Wallman, Dan E. Browne

We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.We consider general settings of Bell inequality experiments with many parties, where each party chooses from a finite number of measurement settings each with a finite number of outcomes. We investigate the constraints that Bell inequalities place upon the correlations possible in local hidden variable theories using a geometrical picture of correlations. We show that local hidden variable theories can be characterized in terms of limited computational expressiveness, which allows us to characterize families of Bell inequalities. The limited computational expressiveness for many settings (each with many outcomes) generalizes previous results about the many-party situation each with a choice of two possible measurements (each with two outcomes). Using this computational picture we present generalizations of the Popescu-Rohrlich nonlocal box for many parties and nonbinary inputs and outputs at each site. Finally, we comment on the effect of preprocessing on measurement data in our generalized setting and show that it becomes problematic outside of the binary setting, in that it allows local hidden variable theories to simulate maximally nonlocal correlations such as those of these generalized Popescu-Rohrlich nonlocal boxes.

arXiv:1108.4798Physical Review ADec 6, 201125 citations

Maximal Extension of an Impossibility Theorem Concerning Quantum Measurement

Howard Stein

Boston studies in the philosophy of scienceJan 1, 19978 citations

Non-locality, Contextuality and Transition sets

Westman, Hans

We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measures of non-local transition sets. We also introduce a new form of contextuality, {\em measurement ordering contextuality}, i.e. there exists commuting operators $\hat{\mathcal{A}}$ and $\hat{\mathcal{B}}$ such that the outcome for $\hat{\mathcal{A}}$ depends on whether we measured $\hat{\mathcal{B}}$ before or after $\hat{\mathcal{A}}$ . It is shown (excluding retro-causal and/or conspiratorial theories) that any hidden variable theory capable of reproducing the quantum statistics has to have this property. This generalizes yet another feature of the hidden variable theory of deBroglie and Bohm.We discuss quantum non-locality and contextuality using the notion of transition sets. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measures of non-local transition sets. We also introduce a new form of contextuality, {\em measurement ordering contextuality}, i.e. there exists commuting operators $\hat{\mathcal{A}}$ and $\hat{\mathcal{B}}$ such that the outcome for $\hat{\mathcal{A}}$ depends on whether we measured $\hat{\mathcal{B}}$ before or after $\hat{\mathcal{A}}$. It is shown (excluding retro-causal and/or conspiratorial theories) that any hidden variable theory capable of reproducing the quantum statistics has to have this property. This generalizes yet another feature of the hidden variable theory of deBroglie and Bohm.

arXiv:0711.2653Nov 16, 20071 citation

On Hidden Variables and Quantum Mechanical Probabilities

Eugene Paul Wigner

Springer eBooksJan 1, 19977 citations

\hat{\mathcal{A}}

and

\hat{\mathcal{B}}

such that the outcome for

\hat{\mathcal{A}}

depends on whether we measured

\hat{\mathcal{B}}

before or after

\hat{\mathcal{A}}

. It is shown (excluding retro-causal and/or conspiratorial theories) that any hidden variable theory capable of reproducing the quantum statistics has to have this property. This generalizes yet another feature of the hidden variable theory of deBroglie and Bohm.