Optimal estimation of an observable's expectation value for pure states   for general measure of deviation
  We investigate the optimal estimation of quantum expectation value of a physical observable, which minimizes a mean error with respect to general measure of deviation, when a finite number of copies of a pure state are prepared. If pure sates are uniformly distributed, the minimum value of mean error for any measure of deviation is achieved by projective measurement on each copy. 
Minoru Horibe, Akihisa Hayashi and Takaaki Hashimoto