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The Einstein-Podolsky-Rosen state maximally violates Bell's inequalities

Hans Halvorson

Published Jan 1, 2000• 23 citations
OpenAlex

Abstract

In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of the EPR state as a normalized, positive linear functional of the Weyl algebra for two degrees of freedom. We then show that the EPR state maximally violates Bell's inequalities.

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This report discusses the following: The analysis of the singlet state of separate fermions proves that the EPR contradicts QM. The violation of special relativity. The Schroedinger equation and the EPR. The conservation of angular momentum. The proposal of collapse. The factorization of the spin states. The superposition principle. No paradox exists within the theory. The original state of Einstein et al is not a valid example of the EPR, and it seems impossible to construct a valid linear momentum example. This is another indication that the EPR contradicts QM. Actions at a distance, the model of Einstein et al for particles with mass, and Bell`s inequalities and their physical meaning.

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We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.

Physical Review A•Nov 1, 1997•24 citations
In their well-known argument against the completeness of quantum theory, Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly correlates the positions and momenta of two particles. We prove the existence and uniqueness of the EPR state as a normalized, positive linear functional of the Weyl algebra for two degrees of freedom. We then show that the EPR state maximally violates Bell's inequalities.
We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-1∕21∕21∕2 as well as spin-1 particles.
The nonlocality of Einstein–Podolsky–Rosen (EPR) states is discussed in the framework of Weyl algebras. To include all possible limits of expectation values, the associated canonical cyclic representations of EPR states are considered. The momentum and position operators of individual particles do not exist in such representations, which explains the uncertainty principle in these cases. However, there are still one-to-one correspondences between the local Weyl operators associated with individual particles. The local observable algebras of individual particles are Type II1 von Neumann algebras and have numerous projection operators. The states obtained by applying local projection operations to the EPR states have perfect correlations between local subalgebras. Bell’s inequality is maximally violated by these states. The lack of atomic projections of Type II1 von Neumann algebras implies that the EPR states cannot be disentangled by local projection operations.
This report discusses the following: The analysis of the singlet state of separate fermions proves that the EPR contradicts QM. The violation of special relativity. The Schroedinger equation and the EPR. The conservation of angular momentum. The proposal of collapse. The factorization of the spin states. The superposition principle. No paradox exists within the theory. The original state of Einstein et al is not a valid example of the EPR, and it seems impossible to construct a valid linear momentum example. This is another indication that the EPR contradicts QM. Actions at a distance, the model of Einstein et al for particles with mass, and Bell's inequalities and their physical meaning.
We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.
This report discusses the following: The analysis of the singlet state of separate fermions proves that the EPR contradicts QM. The violation of special relativity. The Schroedinger equation and the EPR. The conservation of angular momentum. The proposal of collapse. The factorization of the spin states. The superposition principle. No paradox exists within the theory. The original state of Einstein et al is not a valid example of the EPR, and it seems impossible to construct a valid linear momentum example. This is another indication that the EPR contradicts QM. Actions at a distance, the model of Einstein et al for particles with mass, and Bell`s inequalities and their physical meaning.
We examine the properties and behavior of the original Einstein-Podolsky-Rosen (EPR) wave function [Phys. Rev. 47, 777 (1935)] and related Gaussian-correlated wave functions. We assess the degree of entanglement of these wave functions and consider an argument of Bell [Ann. (N.Y.) Acad. Sci. 480, 263 (1986)] based on the Wigner phase-space distribution [Phys. Rev. 40, 749 (1932)], which implies that the original EPR correlations can accommodate a local hidden-variable description. We extend Bell's analysis to the related Gaussian wave functions. We then show that it is possible to identify definite nonlocal aspects for the original EPR state and related states. We describe possible experiments that would demonstrate these nonlocal features through violations of Bell inequalities. The implications of our results, and in particular their relevance for the causal interpretation of quantum mechanics, are considered.