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Chinese Journal of Physics

Robustness of Equalities in Local Realism Violation for Three-Qubit Systems

Fatemeh Shirdel, Hossein Movahhedian

Published Jun 1, 2013• 0 citations
Publisher

Abstract

In this paper our main motivation is a stronger violation of local realism, which may help in the search of Bell expressions tolerating more noise. We will introduce an equality in three-qubit systems which is violated by quantum theory and can tolerate more white and color noise than other inequalities in these systems. We will also calculate the violation factor as defined in [11] and show that it increases in this case.

DOI
10.6122/cjp.51.628

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In this paper our main motivation is a stronger violation of local realism, which may help in the search of Bell expressions tolerating more noise. We will introduce an equality in three-qubit systems which is violated by quantum theory and can tolerate more white and color noise than other inequalities in these systems. We will also calculate the violation factor as defined in [11] and show that it increases in this case.
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 .
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.
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.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
Contrary to the usual assumption that the experimental preparation of pure entangled states can be described by mixed states due to white noise, a more realistic description for polarization-entangled states produced by parametric down-conversion is that they are mixed states due to decoherence in a preferred polarization basis. This distinction between white and colored noise is crucial when we look for maximal violations of Bell's inequalities for two-qubit and two-qutrit entangled states. We find that violations of Bell's inequalities with realistic noise for polarization-entangled photons are extremely robust for colored noise, whereas this is not the case for white noise. In addition, we study the difference between white and colored noise for maximal violations of Bell's inequalities for three- and four-qubit entangled states.