Enhanced Quantum Estimation via Purification
  We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the fidelity of subsequent quantum estimation. Even though we lose some qubits of our finite ensemble the information is concentrated in the remaining purified ones. 
Holger Mack, Dietmar G. Fischer, Matthias Freyberger