Study Of The K-unentangled States

Quantum entanglement is an important physical resource in quantum information science.The research on quantum entanglement mainly includes two aspects: qualitative analysis and quantitative calculation.Qualitative analysis is to identify the separability and entanglement of quantum states,and quantitative calculation is to quantify the amount of entanglement in a given state.Our work is mainly to make qualitative analysis of quantum states.First,we define the notion of k-unentangled states.By using the GHZ states and the Dicke states as the target states,we construct the necessary conditions of the k-unentangled states.The main method is to analyze the k-unentangled states by using the relationship between the elements of density matrix of the 1-unentangled states,and extend the research of n-qubit states to the quantum states of any dimension of n-partite systems.In the first chapter,we mainly introduce the related background knowledge,such as quantum states,density matrix,fully separable states and k-unentangled states.In the second chapter,we analyze the relation between the elements of density matrix of the quantum states,and give the necessary conditions for the n-qubit states to be k-unentangled states by the form of theorem,and then we give a necessary condition of n-qubit fully separable states.In the third chapter,we present a necessary condition that the quantum states of any dimension of n-partite systems are k-unentangled states.Finally we summarize our results.