Unveiling the link between quantum ghost imaging and Grover's quantum searching algorithm

Photonic quantum technologies have become pivotal in the implementation of communication, imaging and computing modalities. Among these applications, quantum ghost imaging (GI) exploits photon correlations to surpass classical limits, with recent advances in spatial-mode encoding and phase imaging. In parallel, all-optical computing offers powerful, passive-light processing capabilities. Here, we explore the intersection of these domains, revealing a conceptual and operational link between GI and Grover's quantum search algorithm (GSA) which is designed to search for elements in an unstructured database. Here, the elements are encoded as phases in the position basis states of photons. To show this, we use entangled photon pairs, with one photon encoding the oracle features while the other photon is used to find the marked element.