  We suggest a quantum measurement model in an ion trap which specifies the
probability distribution of two, distinct internal ground states of a trapped
four-level ion. The external degrees of motion of the four-level ion constitute
the meter which, in turn, is coupled to the environment by engineered
reservoirs. In a previous publication, a similar measurement model was employed
to test decoherence effects on quantum nonlocality in phase space on the basis
of coincidence measurements of the entangled system-meter scheme. Here, we
study the effects of decoherence on the entanglement of formation characterized
by the concurrence. The concurrence of the system enables to find the maximum
possible violation of the Bell inequality. Surprisingly, this model gives
illustrative insights into the question to what extend the Bell inequality can
be considered as a measure of entanglement.
