The Study Of Completely Symmetric States

Quantum entanglement was first recognized by Einstein and Schrodinger.Quantum entanglement and nonlocality are the basic problems in quantum information theory,and play a vital role in the field of quantum computation and quantum information.Quantum nonlocality is one of the most incredible phenomenon of many physics predictions.Bell inequality reveals quantum nonlocality.The people have done a lot of research about the quantum states violation of the Bell's inequality.In the process of research,aiming at general quantum states,people have many problems that are difficult to solve.This is a hindrance to our study of quantum states violation of Bell's inequality.To this end,we decide to start from symmetric quantum states.By studying the violation of symmetric quantum states to Bell's inequality,we consider the violation of general permutationally invariant quantum states to Bell's inequality.Symmetry plays an important role in quantum mechanics.We study a subclass of symmetric quantum states in the multipartite system,namely,the completely symmetric states,which are invariant under any index permutation.In this paper,we mainly study the conditions for 3-qubit completely symmetric pure states,4-qubit completely symmetric pure states,5-qubit completely symmetric pure states and permutationally invariant quantum states,which violate the Bell inequality.In the part one,we introduce some basic knowledge related to the research content of this paper,including quantum state,Bell inequality of multipartite qubit systems,and so on.In the part two,we obtain the conditions for 3-qubit completely symmetric pure states,4-qubit completely symmetric pure states,and 5-qubit completely symmetric pure states violating scalable Bell inequality of multiqubit systems by detailed calculation,and discuss the quantum violation of these quantum states.In the part three,by detailed calculation,we discuss the quantum nonlocality and derive the conditions for general 3-qubit permutationally invariant quantum states,4-qubit permutationally invariant quantum states,and 5-qubit permutationally invariant quantum states violating scalable Bell inequality of multiqubit systems.