Fig. 2
Optimal weak measurement realized in a photonic system. a HWP2 and HWP3 are rotated at θ/2 and π/4 − θ/2 degree determining the strength of measurement F = sin2θ. Photons with vertical polarization state |V〉 transmit calcite beam displacer (BD) without change of its path while photons with horizontal polarization state |H〉 suffer a shift away from its original path. HWP1, HWP4 and HWP5 are rotated at the same degree φ/2 to realize weak measurement of polarization observable σφ = |φ〉〈φ| − |φ⊥〉〈φ⊥|. The measurement outcome +1(−1) is encoded in path 0(1) separately. b The setup, used in actual experiment, realizes same optimal weak measurement as shown above. The only difference is that specific outcome +1(−1) can be selected by rotating HWP1 and HWP4. In the measurement of observation σφ with HWP1 and HWP4 rotated at φ/2 degree, outcome +1 is obtained when photons comes out of the setup and outcome −1 is obtained when HWP1 and HWP4 rotated at φ/2 + π/4. Note that measurement outcome values are extracted in the final coincidence detection
