Polygamy Relation of Quantum Correlations with Equality

Abstract

This study provides a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy relation with equality, it presents polygamy inequalities satisfied by the βth power of the quantum correlation measures. Taking concurrence of assistance as an example, it further illustrates the significance and advantages of these relations. It also obtains a polygamy relation with equality by considering the one‐to‐group entanglements for any quantum entanglement measures that do not satisfy the polygamy relations. It demonstrates that such relations for tripartite states can be generalized to multipartite systems.

Near MDS and near quantum MDS codes via orthogonal arrays

“…Developing advanced quantum technologies may benefit from the present work. Entanglement is essential in quantum communication and quantum information processing [53,54,65]. Among the states of entanglement, quantum uniform states are an important class of multipartite entangled states, as these have been widely applied to QECCs, teleportation, key distribution, dense coding, and quantum computation.…”

“…IrOAs play an important role in the construction of quantum uniform states and QECCs. Quantum entanglement, one of the most important quantum correlations and quantum resources, plays a crucial role in quantum communication and quantum information processing [53,54]. Some open problems on construction of quantum uniform states have been solved by OAs [48][49][50].…”