Entanglement protection and generation under continuous monitoring

Entanglement between two quantum systems is a resource in quantum information, but dissipation usually destroys it. In this article we consider two qubits without direct interaction. We show that, even in cases where the entanglement is destroyed by the open system dynamics, the entanglement can be preserved or created by the mere monitoring of the environment, just by filtering the state of the qubits. While the systems we study are very simple, we can show examples with entanglement protection or entanglement birth, death, rebirth due to monitoring.