Physically realizable entanglement by local continuous measurements

Quantum systems prepared in pure states evolve into mixtures under environmental action. Continuously realizable ensembles (or physically realizable) are the pure state decompositions of those mixtures that can be generated in time through continuous measurements of the environment. Here, we define continuously realizable entanglement as the average entanglement over realizable ensembles. We search for the measurement strategy to maximize and minimize this quantity through observations on the independent environments that cause two qubits to disentangle in time. We then compare it with the entanglement bounds (entanglement of formation and entanglement of assistance) for the unmonitored system. For some relevant noise sources the maximum realizable entanglement coincides with the upper bound, establishing the scheme as an alternative to protect entanglement. However, for local strategies, the lower bound of the unmonitored system is not reached.