The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maximally realistic causal quantum mechanics in $n-$ dimensional configuration space \cite{Roy-Singh1995}. Phase space Bell inequalities and 'Marginal Theorems' \cite{Auberson2002} play a crucial role.The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maximally realistic causal quantum mechanics in $n-$dimensional configuration space \cite{Roy-Singh1995}. Phase space Bell inequalities and 'Marginal Theorems' \cite{Auberson2002} play a crucial role.

arXiv:2301.00119Dec 31, 20220 citations

Bell's inequalities for quantum mechanics

H. E. Andås

Physics Letters AJul 1, 19926 citations

Classical statistical distributions can violate Bell-type inequalities

A. Matzkin

We investigate two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum-mechanical angular-momentum eigenstates. We obtain the phase-space averages of specific observables related to the projection of the particles' angular momentum along axes with different orientations, and show that the ensuing correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the joint measurements whose existence is required in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.We investigate two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum-mechanical angular-momentum eigenstates. We obtain the phase-space averages of specific observables related to the projection of the particles' angular momentum along axes with different orientations, and show that the ensuing correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the joint measurements whose existence is required in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.

arXiv:quant-ph/0703251Journal of Physics A Mathematical and TheoreticalFeb 12, 200811 citations

The Bell inequality in quantum mechanics

Springer eBooksJan 1, 20041 citation

Bell's inequalities and their relevance to the problem of nonlocality in quantum mechanics

Luiz Carlos Ryff

Physics Letters ASep 1, 19862 citations

Probabilistic quantum phase-space simulation of Bell violations and their dynamical evolution

L. Rosales-Zárate, Bogdan Opanchuk, P. D. Drummond +1 more

Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase-space methods, namely, the positive- $P$ representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion and discuss multimode generalizations.Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase-space methods, namely, the positive-$P$ representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion and discuss multimode generalizations.

arXiv:1405.1168Physical Review AAug 13, 201420 citations

n-

dimensional configuration space \cite{Roy-Singh1995}. Phase space Bell inequalities and 'Marginal Theorems' \cite{Auberson2002} play a crucial role.

Quantum simulations of Bell inequality violations are numerically obtained using probabilistic phase-space methods, namely, the positive-

P

representation. In this approach the moments of quantum observables are evaluated as moments of variables that have values outside the normal eigenvalue range. There is thus a parallel with quantum weak measurements and weak values. Nevertheless, the representation is exactly equivalent to quantum mechanics. A number of states violating Bell inequalities are sampled, demonstrating that these quantum paradoxes can be treated with probabilistic methods. We treat quantum dynamics by simulating the time evolution of the Bell state formed via parametric down-conversion and discuss multimode generalizations.