Investigating Quantum Entanglement in Open Systems with Non-Markovian Environmental Interactions

1. Introduction 1.1 Background and Motivation 1.2 Problem Statement 1.3 Objectives 1.4 Structure of the Thesis 2. Quantum Entanglement Basics 2.1 Definition and Properties 2.2 Measurement of Entanglement 2.3 Applications in Quantum Computing 3. Open Quantum Systems 3.1 Definition and Dynamics 3.2 Markovian vs Non-Markovian Systems 3.3 Relevance in Quantum Technologies 4. Non-Markovian Environmental Interactions 4.1 Characterizing Non-Markovianity 4.2 Models and Examples 4.3 Impact on Quantum Coherence 5. Theoretical Framework 5.1 Mathematical Formulation 5.2 Tools and Techniques 5.3 Limitations of Existing Models 6. Methodology 6.1 Experimental Setup 6.2 Data Collection Techniques 6.3 Data Analysis Methods 7. Results and Discussion 7.1 Experimental Findings 7.2 Comparison with Markovian Systems 7.3 Implications for Future Research 8. Conclusion and Future Work 8.1 Summary of Findings 8.2 Contributions to the Field 8.3 Directions for Further Study