Two-qubits in a large-S environment

We analytically express the loss of entanglement between the components of a quantum device due to the generation of quantum correlations with its environment, and show that such loss diminishes when the latter is macroscopic and displays a semi-classical behaviour. We model the problem as a device made of a couple of qubits with a magnetic environment: this choice allows us to implement the above condition of semi-classical macroscopicity in terms of a large-S condition, according to the well known equivalence between classical and $S \rightarrow \infty$ limit. A possible strategy for protecting internal entanglement exploiting the mechanism of domain-formation typical of critical dynamics is also suggested.