  We consider the estimation of two-qubit interactions when initial states of
both qubit can be locally controlled, while the final state of only one qubit
can be measured. This amounts to realize a model of quantum channel
communication with environment assistance. In such a framework the unitaries'
parameters space results a tetrahedron in $\mathbb{R}^3$. On its edges the
problem, becoming of single parameter estimation, can be exactly solved and we
derive optimal probe states and estimators. Our results show that the
possibility of environment assistance is always beneficial, while the usage of
entanglement at channels' input is not.
