Quantum learning algorithms for quantum measurements
  We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information. 
Alessandro Bisio, Giacomo Mauro D'Ariano, Paolo Perinotti, Michal   Sedlak
quant-ph