Quantum Entanglement Of Graph States And The Construstion Of Pauli Entanglement Witness

Recently, with the rapid development of quantum information technology, quantum communication studies that how the qubit carry quantum information transmit in the channel have received wide attention. As we all know, any channel which affected by the external environment or its own channel noise has a negative effect on the transmission of quantum information at some level, therefore, the research about the maximum noise tolerlence of different quantum graph states under various channel models is beneficial to realize quantum communication. In fact, the maximum noise tolerance of various channel models is obtained by measuring the entanglement value of different graph states. Meanwhile, finding the entanglement witnesses regulation and structuring the mathematical formulas of them is very useful to detect multipartite entanglement and the maximum noise tolerance. At present, some scholars have given the maximum noise tolerance and their entanglement witnesses for partly three to six graph states mixed with white noise. However, all of them is for a single quantum state under the most simply channel model.In this paper, we will discuss the maximum noise tolerance and give the entanglement witnesses of bipartite entanglement for all four-qubit and five-qubit graph states under depolarization channel. In addition, we accurate the maximum white noise tolerance for different mixed four-qubit and five-qubit quantum states.The paper introduces the definition of quantum entanglement and describes the three different definitions of graph states and their related properties at first. Then this essay gives the basic concept of entanglement witnesses. What’s more, in this paper, we detail the method of the bipartite entanglement measure for four-qubit and five-qubit graph states, namely the maximum noise under depolarization channel. Meanwhile, we find the regulation of entanglement witnesses which is tracked by some programs and give the correct formulas. Finally, we accurate the maximum noise tolerance of the mixed four-qubit and five-qubit quantum states mixed with white noise.