Weak measurements with completely mixed probe states
  Weak measurements with mixed probe states were investigated in the presence of noise in the probe system. We show that the completely mixed state can be used as a probe state for weak measurements of imaginary weak values. The completely mixed probe state has some advantages in terms of noise tolerance. We also experimentally demonstrated weak measurements of polarization rotation via unpolarized light, which corresponds to weak measurements with completely mixed probe states in a two-state system. 
Shuhei Tamate, Toshihiro Nakanishi and Masao Kitano
quant-ph