Dynamics of two-qubit entanglement in a self-interacting spin-bath

It has recently been shown that interactions among the spins of a bath can result in an effective suppression of the decoherence of a single qubit embedded in a multi-spin environment. However, the effects of such intrabath interaction on the dynamics of entanglement are still not well understood. Here we study the dynamics of a system composed of two entangled qubits coupled to (1) independent self-interacting spin baths, and (2) a common self-interacting spin bath. We find that, as in the case of a single qubit, strong interactions among the spins in the bath may induce an effective decoupling between the bath and the system - this in turn suppresses the loss of entanglement that a non-, or weakly, interacting bath would typically cause. However we find that the intrabath interaction strength needed to achieve such effects is much larger than in the single qubit case, especially when the two qubits share the same environment. Our results illustrate the system's size effects in the entanglement sharing condition, where the entanglement within the bath limits the entanglement between the bath and the system.