Optical homodyne tomography reconstructs an optical quantum state from repeated optical quadrature measurements at different phases. A strong coherent local oscillator interferes with the signal on a beam splitter; balanced homodyne detection subtracts the two detector outputs to estimate the quadrature selected by the reference phase.
Many identically prepared signals give a distribution for that quadrature. Repeating at several phases supplies complementary distributions from which a density matrix or optical Wigner function can be estimated. One quadrature distribution alone generally does not determine the state, just as a single projection of a three-dimensional object does not reveal its full shape. Detector efficiency, mode matching and phase noise must be included in the measurement model; otherwise apparent loss or excess noise can be assigned incorrectly to the signal state.
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