Degree of entanglement in a quantum-measurement process

We suggest a quantum-measurement model in an ion trap that 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 that, 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 us to find the maximum possible violation of the Bell inequality. Surprisingly, this model gives illustrative insights into the question as to what extent the Bell inequality can be considered as a measure of entanglement.