2025,
Urmia university of Technology, Iran,
This thesis investigates the concept of quantum fidelity as a fundamental metric for quantifying the similarity between quantum states, with a particular focus on many-body quantum systems. Quantum fidelity serves as a unifying tool bridging quantum information theory and condensed matter physics, providing valuable insights into the stability, coherence, and robustness of quantum information.
The research explores the mathematical foundations of fidelity, its behavior under various interactions and perturbations, and its role in detecting quantum phase transitions through fidelity susceptibility. Moreover, the study examines the connection between fidelity, entanglement, and information stability, emphasizing how decoherence and environmental coupling influence quantum information preservation in both closed and open quantum systems.
A significant part of the work is devoted to understanding fidelity decay dynamics, Loschmidt echoes, and their relevance to non-thermalization phenomena and quantum many-body scars, which exhibit deviations from the Eigenstate Thermalization Hypothesis (ETH).
Through theoretical analysis and conceptual modeling, this thesis contributes to the broader understanding of information stability, decoherence control, and thermalization behavior in complex quantum systems. The findings have direct implications for developing scalable quantum technologies, including quantum communication, quantum error correction, and simulation of strongly correlated systems.