Genuine Tripartite Bell Nonlocality And Entanglement Witnesses

Since the establishment of quantum mechanics,many people have done a lot of work and study about quantum nonlocality.In 2007,Wiseman,Jones and Doherty classified quantum nonlocality more precisely:quantum entanglement,quantum steering and Bell nonlocality.In this paper,we mainly study two kinds of quantum nonlocality:Bell nonlocality and quantum entanglement.The main findings are as follows:First,we studied the genuine tripartite Bell nonlocality in triple Jaynes-Cummings model.In 1963,Jaynes and Cummings proposed the Jaynes-Cummings model,which is a simple model in quantum optics.We mainly consider the triple Jaynes-Cummings model as the initial states are assumed to be two types of GHZ-like states.According to the Svetlichny inequality,we studied the evolution of their genuine tripartite Bell nonlocality.We select the subsystems ABC,abc,ABc,Abc,ACb and Cab to calculate and analyze them respectively.The analytic expression of genuine tripartite Bell nonlocality is obtained.For three-atom subsystem ABC and three-cavity subsystem abc,we know that there are some time periods in which the two subsystems violate the Svetlichny inequality,that is,they are in genuine tripartite Bell nonlocality.However,for the subsystem of ABc,Abc,ACb and Cab consisted of atoms and cavities,according to our corresponding expressions,for the two kinds of GHZ-like states,they all satisfy the Svetlichny inequality.Second,we studied the genuine tripartite Bell nonlocality of GHZ states in the non-inertial systems.We consider two cases,one observer accelerating and two observers accelerating.At first,we find that when Charlie accelerates,no matter how much the acceleration is,there is always S(?abc?)>4.This means that the subsystem ABC? is always in genuine tripartite Bell nonlocality.But if the observer Charlie's acceleration increases,then the genuine tripartite Bell nonlocality decreases.In the second case,we consider that Alice is at rest,and Bob and Charlie are uniformly accelerating with respect to Alice.We find that for different subsystems,the genuine tripartite Bell nonlocality has different monotonicity about the acceleration parameters rb and rc.As for the MABK inequality,we obtain that all subsystems satisfy this inequality.When we compare the subsystems ABC? and ABC?,AB?C? and AB?C?,we get that when the acceleration increases,the genuine tripartite Bell nonlocality of the region ? de-creases and the region ? increases.If the genuine tripartite Bell nonlocality is considered as resource or information,this means that the acceleration can make the information of region ?‘flows'to the region ?.Finally,we studied the construction of entanglement witnesses.Chruscinski et al.constructed a class of entanglement witnesses by using mutual unbiased bases[Phys.Rev.A,97(3):032318(2018)].But their method is only used to construct entanglement witnesses on Cd(?)Cd.We consider the construction of entan-glement witnesses on Ca(?)Cb for any a,b(a might not be equal to b).We construct a trace-preserving and positive map by using two sets of mutually unbiased bases in the two Hilbert spaces.And then,we obtain a class of entanglement witnesses on Ca(?)Cb and give a special case on C3(?)C4.