Maximum residual strong monogamy inequality for multiqubit entanglement

We establish two inequalities, the weighted strong monogamy (WSM) and the maximum residual strong monogamy (MRSM), which sharpen the generalized Coffman-Kundu-Wootters inequality for multiqubit states. The WSM inequality distinguishes itself from the strong monogamy (SM) conjecture [B. Regula ., ] by using coefficients rather than exponents to modulate the weight allocated to various <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>m</a:mi> </a:math> -partite contributions. In contrast, the MRSM inequality is formulated using only the maximum <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>m</b:mi> </b:math> -partite entanglement. We find that the residual entanglement of the MRSM inequality can effectively distinguish the separable states. We also compare the tightness of various SM inequalities and provide examples using a four-qubit mixed state and a five-qubit pure state to illustrate the MRSM inequality. These examples characterize the trade-off relations among entanglement components involving varying numbers of qubits. Our results provide a rigorous framework to characterize and quantify the monogamy of multipartite entanglement.