The Research Of Full Separability For Four Qubit Cluster Diagonal States

As one of the essential properties of quantum mechanics,quantum entanglement is a very important physical resource in quantum information processing and quantum computation.In both theoretical and experimental researches,multipartite entanglement plays an important role in quantum information theory.How to prove a given quantum state to be entangled or not is the one of the core problems.In the last two decades,great efforts have been made to study the criteria of entanglement.However,up to now,the problem of detecting quantum entanglement has not been completely solved.There is no general method to decide that whether a quantum state is multipartite entangled or separable.All the known multipartite criteria have their particular application scenarios and limitations.In this paper,based on some existing criteria for detecting quantum entanglements we have studied the folly separable criterion for four qubit cluster diagonal states by using entanglement witnesses,with emphasis on the mixed states of two cluster basis states and white noise.The results show that there are three different situations for these states.In one situation we obtained the sufficient condition which is also necessary.We obtained the sufficient and necessary conditions which do not coincide with each other in the other two situations.We have also studied the noise tolerance of the mixed state of three cluster basis states.