| 1 Introduction | 第1-25页 |
| ·Background | 第13-14页 |
| ·Separability Criteria | 第14-19页 |
| ·Some Well Known Necessary Separability Criteria | 第14-16页 |
| ·Some Sufficient Separability Criteria | 第16-17页 |
| ·Some Necessary, and Sufficient Separability Criteria | 第17-19页 |
| ·Entanglement Approach to Invariant under Local Unitary Transformations | 第19-24页 |
| ·Summary on Invariant under Local Unitary Transformations | 第19-21页 |
| ·Invariants Approach to Generic Bipartite Mixed States | 第21-24页 |
| ·Organization of The Thesis | 第24-25页 |
| 2 Preliminaries | 第25-40页 |
| ·Quantum States | 第25-31页 |
| ·The Density Operator | 第31-36页 |
| ·Definition and Properties | 第31-34页 |
| ·Reduced Density Operator | 第34-36页 |
| ·Separability and Entanglement | 第36-38页 |
| ·Separability of Pure States | 第36-37页 |
| ·Separability of Mixed States | 第37-38页 |
| ·PPT States and Partial Transposition | 第38-40页 |
| 3 Separability and Entanglement of PPT States on Multiple Quantum Spaces | 第40-80页 |
| ·Separability and Entanglement in C~2(?)C~3(?)C~N Composite Quantum Systems | 第40-55页 |
| ·Canonical Form and Separability of PPT States on Multiple Quantum Spaces | 第55-76页 |
| ·Canonical Form and Separability of PPT States on Tripartite Quantum Spaces | 第55-67页 |
| ·Canonical Form and Separability of PPT States on Multiple Quantum Spaces | 第67-76页 |
| ·Separability and Entanglement of Identical Bosonic Systems | 第76-78页 |
| ·Summary and Discussion | 第78-80页 |
| 4 Equivalence of Quantum States under Local Unitary Transformations | 第80-97页 |
| ·Invariants for a Class of Tripartite Pure States | 第80-88页 |
| ·Invariants for a Class of Tripartite Mixed States | 第88-96页 |
| ·Summary and Discussion | 第96-97页 |
| References | 第97-100页 |
| List of Publications | 第100-101页 |
| List of Research Projects | 第101-104页 |
| Acknowledgements | 第104-106页 |
