The Separability Of Three Qubit X State

The theoretical basis of quantum information science is the quantum mechanics born in the early 20th century.It is the science that solves the problem that classical mechanics and classical informatics cannot be applied by using the quantum mechanical effects of microscopic particles.Quantum informatics is the interdisciplinary subject of quantum mechanics and information science.It plays a major role in today's society that is increasingly demanding informatization.Nowadays,as the two popular directions in the field of quantum information science,quantum communication and quantum computation have extremely high academic and application value.In the past two decades,quantum information science developed a lot,it has become the scientific field of key development in various countries.As one of the most important physical properties of quantum informatics,quantum entanglement is closely related to many important issues of quantum optics and condensed matter physics,and there are many applications in quantum information processing(QIP):quantum computation,quantum cryptography,quantum teleportation,quantum superdense coding.Therefore,entanglement is one of the core problems in quantum information theory.Deciding whether a given state is entangled and accurately dividing the entanglement and separable boundary are the fundamental problems of quantum information science research.In recent years,people have paid a lot of attentions to the calculation of quantum entanglement,but it is not easy to judge whether a given quantum state is entangled or not.The latest research results show that the determination of quantum entanglement is a NP hard problem.At present,the entanglement problem of two-body quantum states has been well studied,and many very reliable and operational criteria have been developed,the most important of those are Bell inequality and PPT criterion.However,the problem of multiparticle quantum entanglement remains to be studied.It is still difficult to accurately distinguish the fully separable and entangled part of a set of given quantum states.For a general three qubit X state,it is impossible to determine whether it is fully separable or entangled directly from the density matrix.In this paper,an entanglement detection method based on unitary transformation and entanglement witness is proposed.By processing the density matrix of a given three qubit X state,it can finally judge whether it is entangled or not.Different from the previous direct calculation of the density matrix of quantum states,the method firstly performs a unitary transformation on the density matrix of the three qubit X state,and then applies entanglement witnesses and matlab numerical calculations.The qualitative and quantitative results of the entanglement of three qubit X state are obtained.