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arXiv:quant-ph/0611124 · Journal of Physics A Mathematical and Theoretical

Stronger violation of local theories with equalities

Hossein Movahhedian

Published Feb 28, 2007• 1 citation
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Abstract

Bell-type inequalities are used to test local realism against quantum theory. In this paper, we consider a two-party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated by quantum theory by a factor of 1.522 tolerating 0.586 fraction of white noise admixture which is twice that of the previous results.

DOI
10.1088/1751-8113/40/11/018

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Bell-type inequalities are used to test local realism against quantum theory. In this paper, we consider a two-party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated by quantum theory by a factor of 1.522 tolerating 0.586 fraction of white noise admixture which is twice that of the previous results.
So far, various Bell type inequalities have been introduced to test the local realism in tripartite systems. In this article we consider a tripartite system with two measurements in each side and two outputs for each measurement. Then we will introduce a new bell type inequality for this system and we show that this inequality is violated by quantum theory with a violation factor and amount of violation of 3.5 and 2.5 respectively, which exceed those of available inequalities in both cases. Also we will show that the white noise tolerance of this new Bell type expression is 0.5, which agrees with the maximum amount of white noise tolerance of available inequalities up to now.
In this paper we show the new Bell-type inequality for three qubit systems (i.e a tripartite system with two measurements in each side and two outputs for each measurement). This inequality is violated by quantum theory with a factor violation of 3.5 tolerating 0.5 fraction of white noise. Our inequality includes only 19 different joint probabilities whereas in other works it is much more than this. We will also show violation amount of this inequality is 2.5. Note that the maximum violation factor and amount of violation in available inequalities are both 2, also t h e w h i t e n o i s e t o l e r a n c e o f o u r i n e q u a l i t y i s i n a g r e e m e n t w i t h m ax i m um v a l u e c a l c u l a t e d s o f a r . K e y w o r d s--n o n l o c a l i t y ; B e l l i n e q u a l i t y ; a m o u n t o f v i o l a t i o n ; v i o l a t i o n f a c t o r ; w h i t e n o i s e t o l e r a n c e .
We have recently shown that for the special case of a bipartite system with binary inputs and outputs there exist equalities in local theories which are violated by quantum theory. The amount of white noise tolerated by these equalities are twice that of inequalities. In this paper we will first introduce an inequality in bipartite qutrits systems which, if non-maximally entangled state is used instead of maximally entangled state, is violated more strongly by quantum theory. Hence reproducing the results obtained in the literature. We will then prove that our equalities in this case are violated by quantum theory too, and they tolerate much more white noise than inequalities.
Abstract We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility v c.
We investigate the violation factor of the original Bell-Mermin inequality. Until now, we have used an assumption that the results of measurement are . In this case, the maximum violation factor is as follows: and . The quantum predictions by n-partite Greenberger-Horne-Zeilinger state violate the Bell-Mermin inequality by an amount that grows exponentially with n. Recently, a new measurement theory is proposed [K. Nagata and T. Nakamura, International Journal of Theoretical Physics, 49, 162 (2010)]. The values of measurement outcome are . Here we use the new measurement theory. We consider a multipartite GHZ state. We use the original Bell-Mermin inequality. It turns out that the original Bell-Mermin inequality is satisfied irrespective of the number of particles. In this case, the maximum violation factor is as follows: and . Thus the original Bell-Mermin inequality is satisfied by the new measurement theory. We propose the following conjecture: All the two-orthogonal-settings experimental correlation functions admit local realistic theories irrespective of a state if we use the new measurement theory.