Optimal partial estimation of quantum states from several copies
  We derive analytical formula for the optimal trade-off between the mean estimation fidelity and the mean fidelity of the qubit state after a partial measurement on N identically prepared qubits. We also conjecture analytical expression for the optimal fidelity trade-off in case of a partial measurement on N identical copies of a d-level system. 
Ladislav Mista Jr., Jaromir Fiurasek