Quantum Nonlocality In Graph States And Its Applications

Graph state is a kind of very important multipartite quantum entangled state,which is widely used in quantum nonlocality,quantum entanglement,and quantum error correction.We introduce the concept of graph state to study quantum nonlocality and give the optimal solution of graph state for the violation of Hardy-type inequality and the nonlocality without inequality and the corresponding optimal measurement direction of experimental measurement for graph state.In this thesis,we mainly study multipartite Bell nonlocality of graph states.In the third chapter.we numerically calculate the violation of Hardy-type inequality from four to six particle GHZ state(fully connected graph state)and give the maximum quantum violation Q value and the P value of mixed noise.At the same time,we reduce variables of multipartite GHZ state to 8 variables.And the violation of Hardy-type inequality from four to six particle GHZ state is recalculated,and the result is better than that in the previous paper [Wang X.et al.,Phys.Rev.A.94,022110(2016)].In the fourth chapter,we first calculate the real number solutions of four to six particle LC nonequivalent graph states with genuine multipartite nonlocality without inequality.We obtain the real number of solutions of GHZ states and ring graph states.Next,we calculate the complex number solutions of several LC nonequivalent graph states.The results show that most of the violations of the GHZ state are greater than other types of graph States.Interesting,the five particle ring graph states are better than those of five particle GHZ state.Then,we also calculate the solution of Hardy-type without inequality in the other case.The result is the same: the violation of the GHZ state is greater than that of other types of graph states.Finally,we take the GHZ state as an example to compare the violation of the hardy type inequality and the complex solution satisfying the hardy type nonlocality without inequality.We find that in the case of many particles,the inequality violation is close to the solution satisfying the nonlocality without inequality violation.Thus we can use the solution without inequality to estimate the violation of GHZ approximately.In the fifth chapter,we generalize the Cabello theorem of graph states.For some types of graph States,we propose new conditions to construct the BAVN proof of graph states.