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Weak measurements with mixed probe states were investigated in the presenceof noise in the probe system. We show that the completely mixed state can beused as a probe state for weak measurements of imaginary weak values. Thecompletely mixed probe state has some advantages in terms of noise tolerance.We also experimentally demonstrated weak measurements of polarization rotationvia unpolarized light, which corresponds to weak measurements with completelymixed probe states in a two-state system.

Weak measurements with completely mixed probe states