Quantum state reconstruction of an intense polarized optical beam via weak measurement

An alternative experiment scheme of quantum state reconstruction is proposed for an intense polarized optical beam via weak measurement with common elements in laboratories. One of the main differences between our scheme and a previous one is that the homodyne detection of mode quadratures of the unpolarized beam outputs is replaced by inputting orthogonally polarized beams and measuring the polarization of the outputs. The approximated formulas are established to explain the relation between experiment data and the magnitude and phase of a pure state wave function at its quadrature eigenvalues. Some constructive suggestions for users are obtained from the simulation: First, the validating condition of our scheme is that the phase gradient of the state wave function must be continuous at the observable eigenvalues; Second, for more accurate and reliable results, we suggest selecting the initial meter state as a squeezed state, choosing the beam splitter reflectivity as small as possible, and collecting as much data as possible by extending the measurement time; Third, one should avoid the error of measurement basis phase rotation since when this error is higher than 0.2 rad, the fidelity is lower than 0.9, and prevent the error of device readout drift particularly on the meter beam since when this error on the meter beam is higher than 0.02 unit corresponding to the quadrature, the fidelity is lower than 0.9.