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A generalized Bell-Inequality and Decoherence for the K 0 K 0 -System

Beatrix C. Hiesmayr

Published Oct 11, 2000• 9 citations
OpenAlex

Abstract

First a generalized Bell-inequality for dierent times and for dierent quasispin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter [1], if the quantum theory is used to recalculate the probabilities. Next the quantum mechanical probabilities are modied by the decoherence approach which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter , which measures the degree of decoherence. This result is compared with the experimental value [2, 3] of the decoherence parameter deduced from the data of the CPLEAR-experiment [4].

Related papers

A generalized Bell-Inequality and Decoherence for the K^0\bar{K^0}-System

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First a generalized Bell-inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter, if the quantum theory is used to recalculate the probabilities. Next the quantum mechanical probabilities are modified by the decoherence approach which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter ζ, which measures the degree of decoherence. This result is compared with the experimental value of the decoherence parameter ζdeduced from the data of the CPLEAR-experiment.

arXiv:hep-ph/0010108•Oct 11, 2000•0 citations

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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.

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We consider a system of two spin-$\frac{1}{2}$ particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g., a collection of $N$ independent spins), the two-particle system undergoes decoherence. Using a simple model of decoherence, we show that this process has two consequences. First, the maximal amount by which the Clauser-Horne-Shimony-Holt inequality is violated decays to zero. Second, the set of directions of measurement for which the inequality is violated is reduced in the course of decoherence. The volume of that set is bounded above by $\text{const}\ifmmode\times\else\texttimes\fi{}{|r|}^{2}$, where $r$ is the decoherence factor. We obtain similar results for the case when each of the two particles is in interaction with a separate environment.

arXiv:0812.3736•Physical Review A•May 1, 2009•4 citations
First a generalized Bell-inequality for dierent times and for dierent quasispin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter [1], if the quantum theory is used to recalculate the probabilities. Next the quantum mechanical probabilities are modied by the decoherence approach which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter , which measures the degree of decoherence. This result is compared with the experimental value [2, 3] of the decoherence parameter deduced from the data of the CPLEAR-experiment [4].
First a generalized Bell-inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter, if the quantum theory is used to recalculate the probabilities. Next the quantum mechanical probabilities are modified by the decoherence approach which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter ζ, which measures the degree of decoherence. This result is compared with the experimental value of the decoherence parameter ζdeduced from the data of the CPLEAR-experiment.
We investigate Bell inequalities for neutral kaon systems from $\ensuremath{\Phi}$ resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, which means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary ``quasispin'' states and different times; finally, we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin 1/21/21/2 or photon case, which changes considerably the possibility of quantum mechanics to violate the Bell inequality. Examples for special ``quasispin'' states are given, especially those that are sensitive to the CP\mathrm{CP}CP parameters $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}^{\ensuremath{'}}.$
We analyze the premises of recent propositions to test local realism via the Bell inequalities using neutral kaons from $\ensuremath{\Phi}$ resonance decays as entangled Einstein-Podolsky-Rosen pairs. We pay special attention to the derivation of the Bell inequalities, or related expressions, for unstable and oscillating kaon ``quasispin'' states and to the possibility of the actual identification of these states through their associated decay modes. We discuss an indirect method to extract probabilities to find these states by combining experimental information with theoretical input. However, we still find inconsistencies in previous derivations of the Bell inequalities. We show that the identification of the quasispin states via their associated decay mode does not allow the free choice to perform different tests on them, a property which is crucial to establish the validity of any Bell inequality in the context of local realism. In view of this we propose a different kind of Bell inequality in which the free choice or adjustability of the experimental setup is guaranteed. We also show that the proposed inequalities are violated by quantum mechanics.
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.
We consider a system of two spin-12\frac{1}{2}21​ particles, initially in an entangled Bell state. If one of the particles is interacting with an environment (e.g., a collection of NNN independent spins), the two-particle system undergoes decoherence. Using a simple model of decoherence, we show that this process has two consequences. First, the maximal amount by which the Clauser-Horne-Shimony-Holt inequality is violated decays to zero. Second, the set of directions of measurement for which the inequality is violated is reduced in the course of decoherence. The volume of that set is bounded above by $\text{const}\ifmmode\times\else\texttimes\fi{}{|r|}^{2}$, where rrr is the decoherence factor. We obtain similar results for the case when each of the two particles is in interaction with a separate environment.