Research On Graph States Symmetry And Quantum Correlations

Correlations are ubiquitous in nature,and quantum nonlocality is one of the important basis for distinguishing between classical correlations and quantum correlations.The study of quantum nonlocality is also one of the most significant object since the introduction of quantum mechanics.Bell nonlocality is one of the quantum correlations,and it is the important resource in the field of quantum information and quantum communication.The research on Bell nonlocality can generally use the method of Bell’s inequality or no inequality.In this paper,we will use the graph state as the research object,and use the method of Bell’s inequality to study the Bell nonlocality of the graph state.On the basis of the previous graph states,we study a new graph state—W(K)graph state.This type of graph is obtained from some irregular graphs through the LC transformation of graphs,which has strong symmetry,and the form of its Bell operator is also more concise than before the transformation,that is,the symmetry of the graph can be reflected in that its Bell operator also has strong symmetry in terms of structure.For the W(K)type graph state,we use Bell’s inequality to study its Bell nonlocality,and obtain the variation law of the violation value of Bell’s inequality which is related to the number of vertices.Besides,we yielded better results than previous studies by selecting the partial stabilizers of the graph state.On this basis,we also extended the results of Bell’s inequality of the W(K)type graph state,and possibly obtained a higher violation value by adding some additional terms to its Bell operator,which is also useful for future research to some extent.