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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.