Tripartite Quantum Steering Dynamics in Photonic Systems Under Non-Markovian Dynamics

We investigate the non-Markovian dynamics of quantum steering in a tripartite photonic system subject to dephasing noise. By developing a theoretical framework based on the single-photon dephasing model extended to three independent photons, we analyze the temporal evolution of steering measures S^A−BC and S^AB−C for two distinct classes of initial states: W-type entangled states and GHZ-type mixed entangled states. The system is studied under various environmental configurations, ranging from fully Markovian to fully non-Markovian regimes, with asymmetric distributions of memory effects across the three photons. Our results reveal that the dynamics of Gaussian steering are highly sensitive to both the number of photons coupled to non-Markovian environments and the specific partition of the system being considered. For W-states, non-Markovian effects induce oscillatory behavior with death-revival cycles, where the intervals of sudden death and revival amplitudes depend critically on the distribution of memory effects. For GHZ-states, we observe multiple death-revival cycles in some configurations and prolonged preservation of steering without complete sudden death in others. Notably, we find that non-Markovian environments can either enhance steering through information backflow or prove detrimental depending on which subsystems they are coupled to relative to the steering and steered parties. These findings demonstrate that non-Markovianity can serve as a resource for protecting specific types of quantum steering, but its effects are highly configuration-dependent, offering insights for quantum information processing tasks requiring the preservation of directional quantum correlations in photonic networks.