Entanglement fidelity as a measure of preservation of entanglement in local noisy process

A new formula of entanglement fidelity has been introduced, which can serve as a measure of the preservation of entanglement between two initially entangled subsystems exposed to local noisy environments. For a simple model we derive analytic expressions of concurrence and entanglement fidelity and draw the relationship between them. We find that such entanglement fidelity exhibits the behavior similar to that of the concurrence in quantum evolutions.