General monogamy and polygamy properties of quantum systems

The article delves into the fundamental properties of quantum entanglement, specifically the monogamy and polygamy relations that govern the distribution of entanglement in multipartite quantum systems. It begins by highlighting the significance of quantum entanglement in areas such as quantum teleportation and quantum computing. The authors then explore the concept of entanglement monogamy, which limits the entanglement of one subsystem with others in a multipartite system. They discuss the CKW inequality and its generalizations, presenting new monogamy inequalities that are tighter and more accurate than existing ones. The article also introduces the concept of polygamy, which describes the distribution of assisted entanglement in multipartite systems. It presents new polygamy inequalities that complement existing relations, providing a more comprehensive understanding of entanglement distribution. The authors illustrate the advantages of their new inequalities with concrete examples, such as the monogamy relations for concurrence and the polygamy relations for the convex-roof extended negativity. The article concludes by emphasizing the importance of entanglement monogamy in characterizing the distribution of entanglement and highlights the significance of the new monogamy and polygamy relations in describing entanglement under stronger constraints.