Are Quantum Objects Born with Duality?

We study wave-particle duality by exploring for the first time effects of a quantum object's source. A single photon emitted from a pair of nonlocally entangled two-level atoms is specifically analyzed. Surprisingly, duality is found to be a conditional phenomenon depending on the photon's atomic source. It can be tuned maximum, medium, and even minimum (completely absent) by the atomic state purity through an exact quadratic relation that can be called Duality Pythagorean Theorem. The analysis shows a new way of investigating duality by accounting how the single quantum object is created. The result sheds a new light on the fundamental understanding of the completeness of wave-particle duality, and can be tested in various practical physical systems.
Comment: 5 pages, 2 figures