Quantitative complementarity of wave-particle duality

To test the principle of complementarity and wave-particle duality quantitatively, we need a quantum composite system that can be controlled by experimental parameters. Here, we demonstrate that a double-path interferometer consisting of two parametric downconversion crystals seeded by coherent idler fields, where the generated coherent signal photons are used for quantum interference and the conjugate idler fields are used for which-path detectors with controllable fidelity, is useful for elucidating the quantitative complementarity. We show that the quanton source purity μ is tightly bounded by the entanglement E between the quantons and the remaining degrees of freedom by the relation [Formula: see text], which is experimentally confirmed. We further prove that the experimental scheme using two stimulated parametric downconversion processes is an ideal tool for investigating and understanding wave-particle duality and Bohr's complementarity quantitatively.