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We present a systematic framework to quantify the interplay between coherence and wave-particle duality in generic two-path interference systems. Our analysis reveals a closed-form duality ellipse (DE) equality, that rigorously unifies visibility (a traditional waveness measure) and predictability (a particleness measure) with degree of coherence, providing a complete mathematical embodiment of Bohr's complementarity principle. Extending this framework to quantum imaging with undetected photons (QIUP), where both path information and photon interference are inherently linked to spatial object reconstruction, we establish an imaging duality ellipse (IDE) that directly connects wave-particle duality to the object's transmittance profile. This relation enables object characterization through duality measurements alone and remains robust against experimental imperfections such as decoherence and misalignment. Our results advance the fundamental understanding of quantum duality while offering a practical toolkit for optimizing coherence-driven quantum technologies, from imaging to sensing. 

Abstract Wave‐particle duality, intertwining two inherently contradictory properties of quantum systems, remains one of the most conceptually profound aspects of quantum mechanics. By using the concept of energy capacity, the ability of a quantum system to store and extract energy, a device‐independent uncertainty relation is derived for wave‐particle duality. This relation is shown to be independent of both the representation space and the measurement basis of the quantum system. Furthermore, it is experimentally validated that this wave‐particle duality relation using a photon‐based platform. 

We demonstrate super-resolved localization of three point sources with the assistance of a machine learning model that is based on the decomposition of the source signal into Hermite Gaussian modes. High fidelity of over 80% is achieved. 

We explore the equivalence between paraxial optical beam propagation and 2D harmonic oscillator evolution. The phenomenon of quantum state revival of harmonic oscillator is shown to be simulated with the propagation of a focusing beam. 

We experimentally investigate polarization, entanglement, and complementary behavior of a light beam, and the center of mass and moment of inertia of a two-mass system, confirming an unexpected quantitative link between wave optics and mechanics. 

We investigate superresolution of two general point sources using continuous rotation of the observation basis. Optimal superresolution with maximum estimation accuracy is achieved when measurements are performed in the Schmidt basis. 

We investigate super-resolution of two spatially separated practical point sources using machine learning. High fidelity of over 90% is achieved for separations that are 16 times smaller than the conventional resolution limit. 

While optics and mechanics are two distinct branches of physics, they are connected. It is well known that the geometrical/ray treatment of light has direct analogies to mechanical descriptions of particle motion. However, connections between coherence wave optics and classical mechanics are rarely reported. Here we report links of the two through a systematic quantitative analysis of polarization and entanglement, two optical coherence properties under the wave description of light pioneered by Huygens and Fresnel. A generic complementary identity relation is obtained for arbitrary light fields. More surprisingly, through the barycentric coordinate system, optical polarization, entanglement, and their identity relation are shown to be quantitatively associated with the mechanical concepts of center of mass and moment of inertia via the Huygens-Steiner theorem for rigid body rotation. The obtained result bridges coherence wave optics and classical mechanics through the two theories of Huygens.