Minimal measurements of the gate fidelity of a qudit map
  We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed. 
E. Bagan, M. Baig and R. Munoz-Tapia