  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 and we show that, even in cases where the
open system dynamics destroys any initial entanglement, the mere monitoring of
the environment can preserve or create the entanglement, 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.
