Are Quantum Objects Born with Duality?

Single-particle two-path interference has been the dominant scenario employed for analyzing and testing quantum wave-particle duality. It can be regarded as a process of regenerating the quantum object (e.g., a photon, an electron, an atom, etc.) with a two-center source. A natural question arises: will this regeneration process affect the wave and particle natures of the quantum object? To address this question, we analyze the duality property of a photon in relation to the properties of its actual two-point source, i.e., a pair of non-locally entangled two-level atoms. Surprisingly, the photon's duality is found to be solely controlled by the state coherence of the atomic source through an exact Pythagorean relation, $V^2+D^2=\mu^2_S$, where $V$ and $D$ are the single photon's interference visibility and which-way distinguishability respectively and $\mu_S$ is the source state purity. Our analysis opens a new perspective of investigating and understanding quantum duality.