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We study the evolution of the entanglement of noninteracting qubits coupledto reservoirs under monitoring of the reservoirs by means of continuousmeasurements. We calculate the average of the concurrence of the qubitswavefunction over all quantum trajectories. For two qubits coupled toindependent baths subjected to local measurements, this average decaysexponentially with a rate depending on the measurement scheme only. Thiscontrasts with the known disappearance of entanglement after a finite time forthe density matrix in the absence of measurements. For two qubits coupled to acommon bath, the mean concurrence can vanish at discrete times. Our analysisapplies to arbitrary quantum jump or quantum state diffusion dynamics in theMarkov limit. We discuss the best measurement schemes to protect entanglementin specific examples.

Average Entanglement for Markovian Quantum Trajectories