| 摘要 | 第1-7页 |
| Abstract | 第7-11页 |
| 1 Introduction | 第11-18页 |
| 2 Preliminaries | 第18-30页 |
| ·Quantum state | 第18页 |
| ·The tensor product | 第18-21页 |
| ·Definition | 第19-20页 |
| ·Properties of the tensor product | 第20-21页 |
| ·The density matrix or density operator | 第21-25页 |
| ·Definition | 第21-22页 |
| ·Pure state and mixed state | 第22页 |
| ·Unitary freedom in the ensemble for density matrices | 第22-23页 |
| ·Reduced density operator | 第23页 |
| ·The singular value decomposition and the Schmidt decomposition | 第23-25页 |
| ·Separable state | 第25-27页 |
| ·Separable for a pure state | 第25-26页 |
| ·Separable for a mixed state | 第26-27页 |
| ·Concurrence and generalized concurrence | 第27-30页 |
| 3 Separability criteria for quantum mixed states | 第30-55页 |
| ·Separability of rank two quantum states | 第30-39页 |
| ·Canonical form and separability of PPT states | 第39-55页 |
| 4 Lower bounds of concurrence for quantum systems | 第55-68页 |
| ·Lower bounds of concurrence for tripartite quantum systems | 第56-62页 |
| ·Lower bounds of concurrence for multipartite systems | 第62-66页 |
| ·Comparison with the correlation matrix(CM) criterion | 第66-68页 |
| 5 The equivalence of mixed states under local unitary transformations | 第68-76页 |
| ·Equivalence of non-degenerate tripartite states under local unitary transformation | 第68-74页 |
| ·Equivalence of non-degenerate multipartite states under local unitary transformation | 第74-76页 |
| 6 A decomposition of separable Werner states in high-dimensional systems | 第76-83页 |
| ·A decomposition of 3×3 separable Werner states | 第76-80页 |
| ·A decomposition of d×d separable Werner states | 第80-83页 |
| 7 Concluding comments | 第83-85页 |
| References | 第85-91页 |
| Acknowledgements | 第91-92页 |
| List of Publications | 第92页 |
