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arXiv:2111.12367

Tighter monogamy relations for the Tsallis-q and Rényi-$α$ entanglement in multiqubit systems

Rongxia Qi, Yanmin Yang, Jialing Zhang, Wei Chen

Published Nov 24, 2021• 0 citations
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Abstract

Monogamy relations characterize the distributions of quantum entanglement in multipartite systems. In this work, we present some tighter monogamy relations in terms of the power of the Tsallis-q and Rényi-$α$ entanglement in multipartite systems. We show that these new monogamy relations of multipartite entanglement with tighter lower bounds than the existing ones. Furthermore, three examples are given to illustrate the tightness.

DOI
10.48550/arxiv.2111.12367

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Tighter monogamy relations for the Tsallis-q and Rényi-ααα entanglement in multiqubit systems
Monogamy relations characterize the distributions of quantum entanglement in multipartite systems. In this work, we present some tighter monogamy relations in terms of the power of the Tsallis-q and Rényi-ααα entanglement in multipartite systems. We show that these new monogamy relations of multipartite entanglement with tighter lower bounds than the existing ones. Furthermore, three examples are given to illustrate the tightness.
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.
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-qqq entanglement and R\'{e}nyi-α\alphaα entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.
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.