Quantum Entanglement Distribution And Entanglement Monotonic Analysis In Multipartite Systems

As a fundamental problem in quantum information theory,the characterization of entanglement in multipartite systems has attracted a lot of attention in the past two decades.The monogamy inequalities of entanglement distribution in multi-party systems are important tools for characterizing multipartite entanglement.In particular,the multipartite entanglement indicator based on monogamy of entanglement of formation has the ability to detect all the three-qubit entangled states.However,more research is needed to analyze the monotonic property of this kind of multipartite entanglement indicators.Even for three-qubit systems,there are still some open problems.For examples,whether the three-partite entanglement indicator based on entanglement of formation is monotonic in three-qubit pure states,and whether this property is satisfied for the indicator constructed by average residual entanglement in three-qubit mixed states,etc.On the other hand,it is also an important method to study entanglement properties in multipartite systems by analyzing entanglement dynamics and entanglement distribution for typical entangled states.Mixed maximally entangled states are a kind of special bipartite entangled states where each pure state component is the maximal bipartite entangled pure state,and these mixed states can be used to accomplish the perfect quantum teleportation.It has been found that the mixed maximally entangled states with two components in the cavity-reservoir dissipation system can experience the phenomenon of entanglement sudden death,which is quite different from the asymptotical decay behavior of the Bell entangled pure state.For the multi-component mixed maximally entangled state,it is not clear and yet to be clarified that whether the entanglement sudden death will occur in the evolution and whether the monogamy of entanglement distribution is satisfied.This thesis is divided into three chapters.In Chapter I,we introduce the commonest concepts about bipartite entanglement quantification,pure and mixed maximally entangled states,monogamy inequalities of entanglement distribution and the corresponding multipartite entanglement indicators in multi-party systems.In Chapter II,we study the entanglement monotonic property of tripartite entanglement indicators constructed via the monogamy of entanglement of formation,where we find that this kind of entanglement indicators for three-qubit pure sates is not monotonic under local operations and classical communication and the case of indicators for three-qubit mixed states is similar.Finally,in Chapter III,we study the entanglement evolution and entanglement distribution of mixed maximally entangled states with three components in multipartite cavity-reservoir systems.Compared with the situation of two-component case,the evolution of three-component mixed maximally entangled state still experiences the sudden death of entanglement according to our analytic calculation.We also find that the time of entanglement sudden death in two cavities,the entanglement distribution in cavity-reservoir systems,and the value of multipartite entanglement indicator are dependent on the type and the corresponding probability of the third component in the maximally entangled state.