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arXiv:2312.09502 · Laser Physics Letters

Tighter monogamy inequalities of multiqubit entanglement

Jiayi Li, Zhong‐Xi Shen, Shao-Ming Fei

Published Aug 29, 2023• 5 citations
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Abstract

Abstract Multipartite entanglement holds great importance in quantum information processing. The distribution of entanglement among subsystems can be characterized by monogamy relations. Based on the βth power of concurrence and negativity, we provide two new monogamy inequalities. Through detailed examples, we demonstrate that these inequalities are tighter than previous results.

DOI
10.1088/1612-202x/acf36c

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Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence CCC, the entanglement of formation EEE, negativity Nc{N}_{c}Nc​, and Tsallis-qqq entanglement Tq{T}_{q}Tq​. Monogamy relations for the $\ensuremath{\alpha}\mathrm{th}$ power of entanglement have been derived, which are tighter than the existing entanglement monogamy relations for some classes of quantum states. Detailed examples are presented.
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Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.