Probing Non-Markovian Quantum Channels via Hilbert-Schmidt Speed and Fidelity Enhanced Teleportation Protocols

Abstract: The reliable transmission of quantum information remains a central challenge in the presence of environmental noise. In particular, maintaining high teleportation fidelity in open quantum systems is hindered by decoherence, which disrupts quantum coherence and entanglement. Traditional noise mitigation techniques often neglect the rich temporal correlations present in realistic environments. This raises a key question: can non-Markovian memory effects be harnessed to improve the performance of quantum teleportation? In this work, we address this problem by analyzing how non-Markovian dynamics influence teleportation fidelity. We employ a statistical speed approach based on the Hilbert Schmidt norm to witness information backflow and monitor the system's instantaneous evolution rate. Our study focuses on two measurement-based strategies: weak measurement (WM) combined with quantum measurement reversal (QMR), and a hybrid protocol integrating environment-assisted measurement (EAM) with post selection and QMR. Through analytical expressions and detailed numerical simulations, we demonstrate that both strategies can enhance teleportation fidelity under non-Markovian noise. Notably, the EAM-based scheme exhibits superior robustness, achieving high fidelity even without fine-tuned parameters. Our results establish a concrete link between non-Markovian memory effects, statistical speed, and coherence preservation, offering practical insights for the design of resilient quantum communication protocols.