Sensitivity of measurement-based purification processes to inner interactions

The sensitivity of a repeated measurement-based purification scheme to additional undesired couplings is analyzed, focusing on the very simple and archetypical system consisting of two two-level systems interacting with a repeatedly measured one. Several regimes are considered and in the strong coupling limit (i.e., when the coupling constant of the undesired interaction is very large) the occurrence of a quantum Zeno effect is proven to dramatically jeopardize the efficiency of the purification process.