Optimal finite measurements and Gauss quadratures
  We exhibit measurements for optimal state estimation which have a finite number of outcomes. This is achieved by a connection between finite optimal measurements and Gauss quadratures. The example we consider to illustrate this connection is that of state estimation on $N$ qubits, all in a same pure state. Extensions to state estimation of mixed states are also discussed. 
Sofyan Iblisdir and J\'er\'emie Roland