We analyze the entanglement properties of spins (qubits) attached to theboundary of spin chains near quantum critical points, or to dissipativeenvironments, near a boundary critical point, such as Kondo-like systems or thedissipative two level system. In the first case, we show that the properties ofthe entanglement are significantly different from those for bulk spins. Theinfluence of the proximity to a transition is less marked at the boundary. Inthe second case, our results indicate that the entanglement changes abruptly atthe point where coherent quantum oscillations cease to exist. The phasetransition modifies significantly less the entanglement.
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