The Research Of Quantifying Entanglement

The influence of quantum mechanics is huge.It not only changed our understanding of the physical world,but also changed all aspects of modern science and technology.In the environment of the challenge and hindered development of the classic information technology.The interdisciplinary of quantum mechanics and informatics,i.e.,quantum information theory,is like a flood,which injects new impetus into the further development of modern information technology.Many mature quantum information technologies or theories have confirmed that quantum information technology itself will bring profound or even subversive change to classical information technology,because of its inherent advantages based on quantum mechanics.The security,timeliness and rapidity of quantum information technology have been widely concerned.Because of this,the development of quantum information technology in China has been referred to the height of strategic technology,which has aroused great attention from all walks of life,and has made some world-class technological achievements in a certain area.With the breakthroughs of relevant international and domestic core technologies,quantum information technology is bound to usher in a new and socially beneficial stage.However,due to the understanding of quantum mechanics,many theoretical progress in quantum information technology is not smooth,such as quantum entanglement theory,which is regarded as the key resource of quantum information technology.Since the birth and development of quantum mechanics in twentieth Century,quantum entanglement has been widely studied by experts in physics,information science and other fields.A large number of quantum information technologies are based on this nonclassical correlation,such as dense coding,quantum teleportation,and so on.Until today,however,we still have many challenges to the understanding of quantum entanglement,for example,the relationship between entanglement and macro system,how to determine whether a quantum system has quantum entanglement and how to quantitatively describe the key physical resource and so on.This paper is mainly devoted to the research of quantum entanglement measurement.First,we conduct the structure analysis based on the mainstream of pure bipartite entanglement measures,different entanglement measures to carry out the homology analysis,put forward the concept of the same entangled state,and combined with the computer algorithm to find the target state.Second,based on the relationship of entanglement with the uncertainty of quantum system,this paper proposes an entanglement measure based on the difference of informatics entropy.The specific contents are as follows:(1)the study of the same entanglement state based on Schmidt decompositionIn fact,with the development of quantum entanglement theory,the field has developed a great deal of quantum entanglement measures,which is more mature,or widely recognized is about the measures of pure bipartite system,a multipartite system is still at the trial stage.In spite of this,the existence of a large number of entanglement measures based on different physical principles and concepts makes the research environment more chaotic.The comparison of different measures has been carried out.In this paper,the mathematical structure of the mainstream entanglement measure is analyzed,including Von Neumann entanglement entropy,relative entanglement entropy,concurrence,and negativity.The mathematical structure of the current mainstream bipartite entanglement measure is based on the Schmidt coefficient in the Schmidt decomposition.Further,we propose the concept of the same entanglement state,that is,a set of quantum states with the same degree of entanglement under a specific entanglement measure.Furthermore,in order to avoid the computation process of complex linear algebra,we use random Distillation Algorithm to explore the same entangled state in quantum state.In this paper,two groups of same entangled states obtained by the proposed algorithm are enumerated,and a brief analysis is made on the basis of the calculation results.(2)the study of entanglement measure based on entropy differenceIn the research of quantifying entanglement,it is one of the important ideas to use the relation between entanglement and a certain property of quantum systems.As a nonclassical correlation in quantum systems,quantum entanglement has an obvious influence on the uncertainty of the system.Based on the analysis of the relation between the quantum system uncertainty and quantum entanglement,we propose to measure the degree of entanglement based on the information entropy difference between the quantum state and its separable state with the same local property.The separable state with the same local properties is called the related separable state of the quantum state.The concept of disentanglement is introduced as a mathematical tool for finding the related separated states.Furthermore,in the multipartite system,the concept of partial disentanglement is proposed,which is a very meaningful extension for the study of entanglement measures.Because the concept of partial entanglement breaks the barrier that only concerns the overall entanglement of quantum system,and then concerns the entanglement of a subsystem in composite system and the entanglement between subsystems.This paper gives three cases of entanglement measure frameworks,including the measure of overall entanglement of composite system,the measure of a subsystem's entanglement in composite system,and the entanglement measure between subsystems of composite system.Finally,we show that the proposed framework satisfying the basic criteria of proper entanglement measure.