Separability Criteria For Multi-mode Quantum Entanglement Systems

Quantum information science is brand-new interdisciplinary science subject rapidly developed recent years, it is the combination of quantum mechanics and information science. Quantum state having non-classical quantum entanglement phenomenon, quantum information can achieve many new functions surpassing classical information, it could be said that in a large part, the purpose of quantum information researching is to exploit and apply quantum entanglement, so it makes sense to research quantum entanglement.Quantum entanglement is an important physical resource and its quantification becomes a vital subject of quantum information theory. In recent years, quantification of entanglement has attracted great attention. However, only the entanglement of low-dimensional quantum systems, especially that of multipartite quantum systems, remains an open question.The main content of this dissertation is as follows:First, The evolutive course of quantum entanglement is described, such as EPR Paradox and Schr(o|¨)dinger cat and so on. Several typical quantum information protocols are also introduced in order to demonstrate that quantum entanglement is an important physical resource. The general concept of entanglement and entanglement states are given.Second, the separability criteria of bipartite quantum systems and entanglement measure of bipartite quantum systems are described in detail. Two separability criteria based on different calculate of variance of operators is obtained for continuous variable systems by using Heisenberg uncertainty relation and Cauchy-Schwarz inequality. If the separability criteria is violated, the quantum state is entangled. And the two separability criterias were discussed contrastively were operators were position , momentum operator. When the condition was satisfied, one criteria is detect stronger than the other criteria. The two separability criterias are obviously stronger than many others in detection quantum states.