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Journal of Physics A Mathematical and General

Bivalued ‘click’–‘no-click’ probabilities for EPRB spin correlations

A. R. Usha Devi, Swarnamala Sirsi

Published Mar 3, 2005• 1 citation
Publisher

Abstract

We derive non-local bivalued probabilities of click or no-click outcomes—corresponding respectively to detection or no-detection of the particles—where each of the Einstein–Podolsky–Rosen–Bohm (EPRB) pair of particles is observed in only one of the (2s + 1) possible spin projection channels. In the case of observations in maximum spin down channels, our results coincide exactly with those given by Wódkiewicz 3. We analyse the nature of correlation between the click–no-click results with the help of non-local conditional probabilities and information entropies. We observe that the violation of co-planar BC inequalities is essentially due to stronger correlations between the click–no-click outcomes in the spin projection channels |λa| = |λb|. This observation is also supported by spin transmission Bell inequalitites.

DOI
10.1088/0305-4470/38/11/013

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We derive non-local bivalued probabilities of click or no-click outcomes—corresponding respectively to detection or no-detection of the particles—where each of the Einstein–Podolsky–Rosen–Bohm (EPRB) pair of particles is observed in only one of the (2s + 1) possible spin projection channels. In the case of observations in maximum spin down channels, our results coincide exactly with those given by Wódkiewicz 3. We analyse the nature of correlation between the click–no-click results with the help of non-local conditional probabilities and information entropies. We observe that the violation of co-planar BC inequalities is essentially due to stronger correlations between the click–no-click outcomes in the spin projection channels |λa| = |λb|. This observation is also supported by spin transmission Bell inequalitites.
Two aspects of the relativistic version of the Einstein-Podolsky-Rosen-Bohm (EPRB) experiment with massive particles are discussed: (a) a possibility of using the experiment as an implicit test of a relativistic center-of-mass concept, and (b) influence of the relativistic effects on degree of violation of the Bell inequality. The nonrelativistic singlet state average 〈\ensuremath{\psi}|a\ensuremath{\cdot}\ensuremath{\sigma}\ensuremath{\bigotimes}b\ensuremath{\cdot}\ensuremath{\sigma}|\ensuremath{\psi}〉=-a\ensuremath{\cdot}b is relativistically generalized by defining spin via the relativistic center-of-mass operator. The corresponding EPRB average contains relativistic corrections which are stronger in magnitude than standard relativistic phenomena such as the time delay, and can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with relativistic massive spin- particles. The degree of violation of the Bell inequality is shown to depend on the velocity of the pair of spin- particles with respect to the laboratory. Experimental confirmation of the relativistic formula would indicate that for relativistic nonzero-spin particles centers of mass and charge do not coincide. The result may have implications for quantum cryptography based on massive particles.
We report a new two-photon polarization correlation experiment for realizing the Einstein-Podolsky-Rosen-Bohm (EPRB) state and for testing Bell-type inequalities. We use the pair of orthogonally-polarized light quanta generated in Type 2 parametric down conversion. Using 1 nm interference filters in front of our detectors, we observe from the output of a 0.5mm beta - BaB2O4 (BBO) crystal the EPRB correlations in coincidence counts, and measure an associated Bell inequality violation of 22 standard deviations. The quantum state of the photon pair is a polarization analog of the spin-1/2 singlet state.
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.
The long-standing puzzle of the nonlocal Einstein-Podolsky-Rosen correlations is resolved. The correct quantum mechanical correlations arise for the case of entangled particles when strict locality is assumed for the probability amplitudes instead of locality for probabilities. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Sixty five years ago, the most significant paper questioning a fundamental aspect of quantum phenomena was written by Einstein, Podolsky and Rosen (EPR) [1]. They addressed the question whether the wave-function represented a complete description of reality in quantum mechanics, and argued that it didn’t. Bohr’s reply to this paper [2] was not sufficient to resolve the fundamental issues raised by EPR. Decades later, Bohm rephrased the EPR problem [3] in terms of particles correlated in their spin and this helped enormously in analyzing the problem with clarity. John Bell analyzed the EPR problem in the early sixties and established the Bell’s inequalities obeyed by
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.