Estimation of a quantum interaction parameter using weak measurements:   Theory and experiment
  We investigate the estimation of a small interaction parameter from the outcomes of weak quantum measurements implemented by the interaction. The relation of weak values and sensitivity is explained and the different contributions of postselected results are identified using experimental data. The results show how weak values can be used to control the distribution of input state sensitivity between different postselected outcomes. 
Holger F. Hofmann, Michael E. Goggin, Marcelo P. Almeida, and Marco   Barbieri
quant-ph