Unified monogamy relation of entanglement measures

Abstract

The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our goal in this work is to propose general monogamy inequalities for several entanglement measures on entangled qubit systems. The present results provide a unified model for various entanglement measures including the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, Renyi-q entropy, and Unified-(q, s) entropy. We then propose tightened monogamy inequalities for multipartite qubit systems and derive upper bounds of aforementioned entanglement measures for multipartite pure state under generalized bipartitions. We finally prove a generic result that most of tripartite high-dimensional entangled pure states have no entanglement monogamy. These results are useful for exploring the entanglement theory, quantum information processing and secure quantum communication.