Evolution of biphoton states in ghost imaging with multiple objects

Quantum ghost imaging (GI) has significantly advanced the research and application of spatially entangled photon pairs over the past three decades. Nevertheless, existing works predominantly concentrate on qualitative analyses of GI results. The absence of rigorous theoretical models limits the capability of GI to address quantitative problems, which is essential in complex scenarios. Here, we present a comprehensive theoretical model that describes the evolution of the biphoton state throughout the GI process. Based on this model, we can explicitly analyze how the biphoton state evolves, and how object information is encoded into two-photon correlation measurements. We further introduce a virtual single-arm (VSA) operator, which maps the effects of two-arm optical elements into an equivalent single-arm representation, enabling a more intuitive analysis of biphoton-state evolution. Experimental validation is performed using a GI system based on an intensified charge-coupled device (ICCD) camera with multiple objects placed at different longitudinal positions. The excellent agreement between experimental and simulation results confirms the validity of the theoretical framework. This work clarifies the evolution of the biphoton states in quantum GI and opens new avenues for its applications in GI and broader quantum information tasks.