Monogamy relations of quantum entanglement for partially coherently superposed states**Project partially supported by the National Key Research and Development Program of China (Grant No. 2016YFB1000902), the National Natural Science Foundation of China (Grant Nos. 61232015, 61472412, and 61621003), the Beijing Science and Technology Project (2016), Tsinghua-Tencent-AMSS-Joint Project (2016), and the Key Laboratory of Mathematics Mechanization Project: Quantum Computing and Quantum

Abstract

Monogamy is a fundamental property of multi-partite entangled states. Recently, Kim J S [Phys. Rev. A 93 032331] showed that a partially coherent superposition (PCS) of a generalized W-class state and the vacuum saturates the strong monogamy inequality proposed by Regula B et al. [Phys. Rev. Lett. 113 110501] in terms of squared convex roof extended negativity; and this fact may present that this class of states are good candidates for studying the monogamy of entanglement. Hence in this paper, we will investigate the monogamy relations for the PCS states. We first present some properties of the PCS states that are useful for providing our main theorems. Then we present several monogamy inequalities for the PCS states in terms of some entanglement measures.