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arXiv:2006.08853 · Chinese Physics B

Tighter constraints of multiqubit entanglement in terms of Rényi-α entropy*

Meng-Li Guo, Bo Li, Zhi-Xi Wang, Shao-Ming Fei

Published Apr 29, 2020• 8 citations
arXivHTMLPDF

Abstract

Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the μ-th power of the entanglement measure based on Rényi-α entropy, as well as polygamy relations in terms of the μ-th power of Rényi-α entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones.

DOI
10.1088/1674-1056/ab8e2e

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Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the μ-th power of the entanglement measure based on Rényi-α entropy, as well as polygamy relations in terms of the μ-th power of Rényi-α entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones.
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.
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide a characterization of multiqubit entanglement constraints in terms of unified-(q, s) entropy. A class of tighter monogamy inequalities of multiqubit entanglement based on the α-th power of unified-(q, s) entanglement for α ≥ 1 and a class of polygamy inequalities in terms of the β-th power of unified-(q, s) entanglement of assistance are established in this paper. Our results present a general class of the monogamy and polygamy relations for bipartite entanglement measures based on unified-(q, s) entropy, which are tighter than the existing ones. What is more, some usual monogamy and polygamy relations, such as monogamy and polygamy relations based on entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance, can be obtained from these results by choosing appropriate parameters (q, s) in unified-(q, s) entropy entanglement. Typical examples are also presented for illustration.
Abstract The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi- α entanglement (R α E) and polygamy relations related to the R α E of assistance (R α EoA). We present new entanglement monogamy relations satisfied by the η -th ( η ≥ 2) power of R α E for α ≥ 2, and by the γ -th ( γ ≥ 4) power of R α E for 7 − 1 2 ≤ α < 2 , respectively. Moreover, we present polygamy relations satisfied by the t th power of R α EoA with 7 − 1 2 ≤ α < 13 − 1 2 for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of R α E and R α EoA, and the three tangle based on our general monogamy relations.
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.