Discussion On The Monogamy Relations Of Quantum Correlation And The Superadditivity Relations Of Quantum Coherence

Quantum correlations and quantum coherence are two fundamental concepts in quantum theory.Quantum correlations characterize the quantum features of a bi-partite or multipartite system,while quantum coherence was defined for the integral system.Moreover,from a practical point of view,quantum correlations and quantum coherence are also invaluable physical resources for quantum information and compu-tation tasks.A successful and secure quantum network relies on quantum correlations distributed among the subsystems,which erose the problem of distributions of quan-tum correlations.Monogamy relation of quantum entanglement characterizes such correlation distributions.In this paper,we mainly study the monogamy relation of quantum correlation and the superadditivity relation of quantum coherence.We mainly conduct research from the following aspects:First of all,in the research process,we get a better inequality relationship than before;Secondly,this inequality relationship is used to optimize the monogamy relationship of monogamy and negativity;Thirdly,we study the gener-alized monogamy relationship of monogamy and negativity,and this result can also be optimized by using the inequality relationship;Fourthly,we investigate relations satisfied by the concurrence of assistance and the negativity of assistance,and an-alytical monogamy inequalities are presented for both concurrence of assistance and negativity of assistance,which are shown to be tighter than the existing ones;Finally,we investigate superadditivity relations related to the l₁ norm of coherence Cl1.The specific content of this article is arranged as follows:Firstly,we introduce the research purpose,research significance,research back-ground,research significance and framework of this article,and introduce some basic knowledge,then basic concepts related to this article.Secondly,in the study of the monogamy relation of quantum correlation,we found that some inequalities are mainly used in the previous literature to optimize the monogamy result of quantum correlation,and then we prove an inequality relation,which is better than the previous inequality results,and we can see that our results are better by drawing comparison;Then we prove a more general inequality relation,which can continue to optimize our results.Thirdly,we study the monogamy relation of quantum correlation in multiqubit system.This paper introduces the monogamy relation of concurrence C and negativ-ity Nc,and optimizes concurrency and negativity twice by using the two inequality relations we got,and gets better results than before;We also study the generalized monogamy relations of concurrence and negativity,and we can also use our inequality relationship to optimize the results.Fourthly,we investigate the monogamy relations satisfied by the concurrence of assistance and the negativity of assistance for multiqubit generalized W-class states.Nalytical monogamy inequalities are presented for both concurrence of assistance and negativity of assistance,which are shown to be tighter than the existing ones.By taking the 4-qubit W class state as an example,and drawing a picture to show that our results are better than previous results.Finally,among the appropriate measures of quantum coherence,the l1 norm of coherence is a widely known coherence measure and easy to use quantifiers.Superad-ditivity relations characterize the distributions of coherence in multipartite quantum systems.We investigate superadditivity relations related to the l1 norm of coher-ence Cl1 and present new analytical superadditivity inequalities for Cl1,examples and drawings show that these inequalities are better than the existing results.