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

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 \zeta, which measures the degree of decoherence. This result is compared with the experimental value of the decoherence parameter \zeta deduced from the data of the CPLEAR-experiment.