Study On Quantum Entanglement And Entanglement Transformation

This dissertation does a research in the measure of quantum entanglement,its property and entanglement transformation. The main content of this dissertation is as follows:This dissertation introduces in details the basic conditions that bipartite entanglement measure should satisfy and the five entanglement measure,von Neumann entropy,formation of entanglement,distillation of entanglement,relative entropy of entanglement and entanglement monotone. This dissertation presents that for a class of states,their relative entropy can be calculated analytically.This dissertation proves that formation of entanglement is smaller than mutual information. As a by-product,this dissertation also proves that there does not exist this kind of quantum state whose nearest separable state is the product of its two reduced density matrices except the state whose classical correlation is zero.This dissertation discusses the evolution of one subsystem under local operation on another entangled subsystem and derives a general formula of the evolution under the PS operation (postselection) on another entangled subsystem. Based on this formula,the remote state preparation and state purification with some probability are discussed.Based on Nielsen theorem of bipartite pure-state transformation under local operation and classical communication (LOCC),the dissertation shows that quantum entanglement can be used to accomplish state transformation and proves that the information in the two product systems can be transferred under LOCC.With the aid of ancilla,the sufficient condition and local operation strategy for state transformation from entangled pure states to entangled mixed states under LOCC arepresent.This dissertation derives the transformation rule between Schmidt decomposable multipartite entangled pure states (Schmidt state) under LOCC,which is the same as the rule for the bipartite entangled pure-state transformation under LOCC.This dissertation proves that a single m -partite entangled mixed state in the system whose dimension of each subsystem is two cannot be purified to an m -partite entangled pure state. In general,a single m -partite entangled mixed state whose density matrix has higher rank cannot be purified to an m-partite entangled pure state. For a class of entangled mixed states,its fidelity cannot be increased under LOCC.This dissertation discusses the transformation rule for three-qubit pure states under LOCC and derives a necessary condition for the transformation between W states with probability one. Meanwhile,some property concerned with the generalized measurement of the transformation is present. This dissertation also proves that any non-Schmidt three-qubit pure state belonging to GHZ class cannot be deterministically transformed to any Schmidt state under LOCC.