The Research On Multipartite Entanglement Of Superpositions

As a kind of very important physical resource, quantum entanglement has a key role in many applications of quantum information theory. As a cornerstone of quantum mechanics, the superposition principle plays key roles in quantum information processing, and is tightly related to some quantum phenomena. What happens to the entanglement of superpositions, and how to measure?In this thesis, we mainly study the multipartite entanglement of superpositions. First of all, we summarize some useful background knowledge and concept. Secondly, we particularly introduce two entanglement measures used for bipartite quantum states, concurrence and negativity. Concurrence and negativity have a close relationship. Based on concurrence, we define two multipartite entanglement measures : one is for the usual multipartite entanglement;another is a genuine multipartite entanglement. We then apply the two measures to study entanglement in superpositions of multipartite pure states of arbitrary dimension. We give the bounds for the usual multipartite entanglement negativity and bounds for genuine multipartite entanglement negativity. Finally, we enumerate one example, the superpositions of n-partite GHZ states and n-partite W state, and calculate the bounds for the usual multipartite entanglement negativity of these states.