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  • Open Access

Maximum residual strong monogamy inequality for multiqubit entanglement

Dong-Dong Dong1, Xue-Ke Song1, Liu Ye1, Dong Wang1,*, and Gerardo Adesso2,†

  • 1School of Physics, Anhui University, Hefei 230601, People's Republic of China
  • 2School of Mathematical Sciences and Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

  • *Contact author: dwang@ahu.edu.cn
  • †Contact author: gerardo.adesso@nottingham.ac.uk
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Phys. Rev. A 113, 022444 – Published 24 February, 2026

DOI: https://doi.org/10.1103/ppcz-znyt

Abstract

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 et al., 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.

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Phys. Rev. A 113, 022444– Published 24 February, 2026
  • Received 29 April 2025
  • Revised 11 December 2025
  • Accepted 9 February 2026
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