Relations Among κ-ME Concurrence, Negative And Polynomial Invariants For The Pure States Of 3-Qubit And 4-Qubit

Entanglement as a special physical resource plays an important role in quantum com-putation and quantum information. The classification of entanglement is one of the main tasks in quantum information. Invariant is an important factor in entanglement classifica-tion. Quantitative relations among invariants, such as the relation between entanglement measure and polynomial invariants, have been widely concerned. The research on the relation of entanglement measure and invariants is of great value.In this paper we mainly study the relations among k-ME concurrence, negativity and polynomial invariants. There are four chapters in this paper. It is organized as follows.In the first chapter we introduce some concepts and theorems. In the second chapter we obtain the relations among k-ME concurrence, polynomial invariants and negativity for the 3-qubit state|ψ>.As we all known there exist nine families of 4-qubit states under the action of s-tochastic local quantum operations assisted by classical communication (SLOCC). In the third chapter we get the relations among k-ME concurrence, polynomial invariants and negativity for the representative states of the nine families. Nevertheless, for some qubits, only when the parameters satisfy certain conditions was the relation established,In the end, we give the relation between k-ME concurrence and τij for W state.