Quantum Forensics: Inferring Photon States via Environmental Bow Waves

This paper presents a rigorous theoretical framework for indirectly reconstructing latent quantum photon states through the analysis of secondary environmental perturbations, termed topological bow waves, induced within a surrounding topological medium. Building upon foundational principles from quantum state tomography and environment-assisted measurement, this approach leverages the environment not as a source of noise but as an active, information-preserving witness to photon interactions. By integrating topological invariants such as Chern numbers and Berry curvature into a multi-witness joint optimization model, the framework enhances state identifiability and suppresses measurement degeneracy. Employing coupled transformation cascades and advanced probabilistic inference methods, including iterative gradient descent and Bayesian fusion, the model enables reconstruction of photon properties—such as number, polarization, frequency, and path—without direct photon absorption or collapse of the quantum state. This work extends prior conceptual tools in photon pulse reconstruction toward a controlled, mathematically rigorous methodology for observing otherwise inaccessible quantum information encoded in environmental responses, opening new avenues for quantum forensics and topological quantum photonics