Liouvillian effective process reconstruction of single qutrit atomic system based on quantum process tomography

Quantum Process Tomography (QPT) is a widely used technique for fully characterizing and reconstructing an unknown quantum process, such as relaxation or quantum-logic operations, by analyzing its effect on a set of initial quantum states. However, conventional QPT methods often overlook the underlying pathways—governed by time-dependent interactions—that drive the evolution from an initial state to a specific final state. In this work, we address this limitation by integrating QPT with the Liouvillian master equation, enabling the reconstruction of the complete dynamics of a quantum system. This approach allows us to extract not only the effective quantum process but also the underlying Hamiltonian and relaxation mechanisms induced by environmental interactions. By combining these tools, we aim to provide a more comprehensive understanding of quantum dynamics, paving the way for improved characterization and control of quantum systems in the presence of noise and decoherence.