Study On The Tripartite Separability Of Noisy Dicke States

Quantum information is the combination of quantum physics and information science.It is also one of the most popular scientific research fields in the world.Our country has reached the world's leading level in some fields of quantum communication and quantum computing.More and more researchers pay attention to quantum information processing and quantum computing.Quantum entanglement is considered to be the most peculiar characteristic of quantum mechanics,which plays an important role in the field of information and communication,and is one of the most important resources in quantum information.Therefore,the study of quantum entanglement has not only profound theoretical significance,but also important practical value.However,the quantum entanglement is often destroyed by noise(the simplest is white noise)in the process of use.The quantum entanglement plus a certain degree of noise will make the quantum entanglement separable,and will also make the quantum entangled state lose the quantum entanglement characteristics.Therefore,it is very important to find the minimum white noise tolerance for a particular entangled state.In addition,because the quantum entanglement mainly involves the multi qubit entanglement,in which the W state and the Dicke state are not only very vulnerable to the influence of white noise,but also one of the most common quantum entangled states in quantum computation and quantum communication,so this paper chooses the four qubit W state and the Dicke state to study the minimum white noise tolerance of the tripartite separability.This paper mainly introduces the research background and significance of quantum entanglement,introduces some basic knowledge of quantum operation,the concept of quantum state theory,density matrix and entanglement witness that will be used in the research of quantum entanglement.The general methods of studying quantum entanglement are summarized by a specific example,and the feasibility of applying the research methods of entanglement witness to multi qubit states is also illustrated.The main contents of this paper are: the study of the tripartite separability of W state and Dicke state and their mixed states under white noise,and the necessity and sufficiency of it are studied and compared.There is no research on the tripartite separability of these two quantum states in the literature at home and abroad.The method used in this paper is based on the entanglement witness,using the method of mutual verification of the necessity of iterative computation and the sufficiency of construction.The results show that the necessary conditions for the tripartite separability almost coincide with the sufficient conditions for the four qubit W state,Dicke state and white noise mixed state,which proves the effectiveness of the method.