Maximum residual strong monogamy inequality for multiqubit entanglement

TL;DR

This paper introduces new inequalities, WSM and MRSM, that improve the understanding of multiqubit entanglement monogamy, providing a rigorous framework for quantification and differentiation of entangled states.

Contribution

The paper presents the maximum residual strong monogamy (MRSM) inequality, sharpening existing inequalities and effectively distinguishing separable states in multiqubit systems.

Findings

MRSM inequality effectively distinguishes separable states.

Comparison shows MRSM provides tighter bounds than previous inequalities.

Examples illustrate trade-offs among entanglement components.

Abstract

We establish two new inequalities, the weighted strong monogamy (WSM) and the maximum residual strong monogamy (MRSM), which sharpen the generalized Coffman-Kundu-Wootters inequity for multiqubit states. The WSM inequality distinguishes itself from the strong monogamy (SM) conjecture [Phys. Rev. Lett. 113, 110501 (2014)] by using coefficients rather than exponents to modulate the weight allocated to various m-partite contributions. In contrast, the MRSM inequality is formulated using only the maximum m-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.