Multipartite monogamy of entanglement for three qubit states

Abstract The distribution of entanglement in a multiparty system can be described by the principle of monogamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among more than two parties. In this work, our aim is to explore how quantum entanglement is distributed in accordance with monogamy relations, which utilize both genuine multipartite entanglement measures and bipartite entanglement measures. Specifically, we treat the source entanglement or the accessible entanglement as genuine multipartite entanglement measures and use the entanglement of formation for bipartite cases. For GHZ class states, we analytically demonstrate that the square of the source entanglement serves as an upper bound for the sum of the squares of the entanglement of formation of the reduced subsystems, with some exceptions in specific non-generic GHZ states. We will also present numerical evidence supporting this result for W-class states. In addition, we also explore the monogamy relationship by using accessible entanglement as an upper bound. Our analysis reveals an opposite but consistent pattern in the behavior of monogamy depending on whether source entanglement or accessible entanglement is used as the upper bound. This pattern emphasizes the dual nature of these two measures.