  We address the problem of the robustness of entanglement of bipartite systems
(qubits) interacting with dynamically independent environments. In particular,
we focus on characterization of so-called local entanglement-annihilating
two-qubit channels, which set the maximum permissible noise level allowing to
perform entanglement-enabled experiments. The differences, but also subtle
relations between entanglement-breaking and local entanglement-annihilating
channels are emphasized. A detailed characterization of latter ones is provided
for a variety of channels including depolarizing, unital, (generalized)
amplitude-damping, and extremal channels. We consider also the convexity
structure of local entanglement-annihilating qubit channels and introduce a
concept of entanglement-annihilation duality.
