The Study On Entanglement Degree Of Quantum

Based on the principle of superposition of states，quantum entanglement isconsidered to consist of strong relationship of nonlocality、non-classical between twoor several quantum systems. It involves in several basic questions of quantummechanics including factuality、localization、hidden variable and measurement theoryand so on. The theory of entanglement tries to give answers to fundamental questionsas:(1) how to distinguish whether a quantum state is an entangled state;(2) how tocharacterize, measure and quantify entanglement. And it not only promotes thedevelopment of quantum mechanics，but also plays an important role in quantumcomputing and quantum communicating.With the development of quantum mechanical theory and quantum informationtechnology，separability criterions which could be used to judge whether a quantum isentangled or separable have been proposed constantly. However, these criterions canonly judge the separability of certain quantum state partly. For this reason, this paperexplore to study on separability criterions:One is analyzing and researching the quantum models of the SU (2)algebraand the SU (1,1) algebra. Building a new more-modes model and Obtaining the newconditions of separability criterions by means of using Heisenberg uncertainty relation,Schrodinger-Robertson uncertainty relation and partial transposition.Another is that deriving a class of inequalities for detecting entanglement inthree-mode states, higher-order three-mode states and multimode states ofSU (2)algebra and SU (1,1) algebra, respectively. Furthermore, these inequalities fordetecting the degree of entanglement are analyzed.Certain theory basis is provided for more comprehensive separability criterionsfrom the two parts of work.