Research On Multipartite Quantum Non-locality With Hardy's Paradox

There is strong correlation between the state of particles that induced by associated collapse of the wave function of two or more particles in quantum mechanics.Such correlation still exists even though the particles are space-like separated,so people usually called such phenomena as non-locality.The non-locality is one of the biggest contradictions between Quantum mechanics and Relativity theory,the study of such phenomena will make significant contributions to the development of basics physics.We are not trying to solve this contradiction in this thesis,while focus on the form of non-locality in multipartite system.With the help of the scheme of the classification of multipartite non-locality based on different hierarchy,we formulated the corresponding local hidden variable model,then,the Hardy's paradox to detect the hierarchy of multipartite nonlocality(HMLN,Hierarchy of Multipartite Non-locality)is derived.Our proposal is a generalization of Hardy's paradox,which makes it can be used for the detection of HMNL,in such way,the older Hardy's paradox is included in the problem we are considering.Our proposal can be classified into two classes,both of them can be used to detect HMNL.The first one,all the Hardy's conditions are joint probability distribution of all particles;while for the second one,some of Hardy's conditions only involve the joint probability distribution of some of particles,we called it Local Hardy's paradox for brevity.For the first class,we find that the generalized entangled GHZ state exhibits Hardy's non-locality for each rank of multipartite non-locality,and the corresponding Bell-type inequality is more efficient compared to the previous work.For local Hardy's paradox,the state that exhibits local Hardy's non-locality should have special entanglement property,while both the generalized GHZ state and W state don't exhibit local Hardy's non-locality.We proposed a genuine entangled symmetry state that exhibits local Hardy's non-locality,the numerical results shows that the visibility threshold of the Bell-type inequality corresponds to the first class Hardy's paradox is decrease so fast as the number of particles increases for this state.The results of our study give insights of the theoretical study on multipartite non-locality,and provide the instruction of the related experimental study.