Wave-particle duality ellipse and application in quantum imaging with undetected photons

TL;DR

This paper introduces a mathematical framework linking wave-particle duality and coherence in two-path systems, applying it to quantum imaging with undetected photons to enable object characterization through duality measurements.

Contribution

It develops a duality ellipse equality unifying visibility, predictability, and coherence, and extends this to quantum imaging, providing a new method for object characterization based on duality.

Findings

Derived a closed-form duality ellipse (DE) equality.

Established an imaging duality ellipse (IDE) relating duality to object transmittance.

Demonstrated robustness of the framework against experimental imperfections.

Abstract

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.