Entanglement distribution in multi-particle systems in terms of unified entropy

Luo, Yu; Zhang, Fugang; Li, Yongming

doi:10.1038/s41598-017-01286-2

Cited by 8 publications

(5 citation statements)

References 43 publications

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“…Theorem 2 gives another monogamy relation based on the entanglement measure UE. Comparing inequality (11) in Theorem 1 with inequality (15) in Theorem 2, one may notice that inequality (11) is better than inequality (15). However, we note that for those classes of states that do not satisfy the conditions in Theorem 1, Theorem 2 is better.…”

Section: Tighter Monogamy Relations Of Multiqubit For Unified Entropymentioning

confidence: 86%

“…For 0 < α < 1, inequality (27) in Theorem 5 gives a new class of monogamy inequality, which is complementary to inequality (15) of Theorem 2 in different region of parameter α. Theorem 5 assumes that E q,s (ρ AB i ) ≤ ∑ N−1 k=i+1 E q,s (ρ AB k ) and E q,s (ρ AB j ) ≥ ∑ N−1 k= j+1 E q,s (ρ AB j ) are partially satisfied for the 2…”

Section: -6mentioning

confidence: 92%

“…[27] for α = 1. For α > 1, (2 α − 1) m > α m , and all 1 ≤ m ≤ N − 3, formula (15) in Theorem 2 leads to a tighter monogamy relation with larger lower bounds than Eqs. ( 9) and (37) in Ref.…”

Section: Tighter Monogamy Relations Of Multiqubit For Unified Entropymentioning

confidence: 97%

“…[12] Later on, many other forms of monogamy relations were established, including those for multiqubit and high-dimensional systems. [13][14][15][16][17][18][19][20][21][22] Recently, in Refs. [23,24], the authors gave an alternative definition of the monogamy relation with no inequality employed.…”

Section: Introductionmentioning

confidence: 99%

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Monogamy and polygamy relations of multiqubit entanglement based on unified entropy*

Jin

Qiao

2020

Chinese Phys. B

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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.

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Section: Tighter Monogamy Relations Of Multiqubit For Unified Entropymentioning

confidence: 86%

Section: -6mentioning

confidence: 92%

Section: Tighter Monogamy Relations Of Multiqubit For Unified Entropymentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Monogamy and polygamy relations of multiqubit entanglement based on unified entropy*

Jin

Qiao

2020

Chinese Phys. B

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“…The unified-(q, s) entropy has a broadly physical meaning that it finds applications, such as, from characterizing quantum channels, studying of complexity beyond scrambling to witnessing entanglement, and so on. [28][29][30][31] Basing unified-(q, s) entropy, the entanglement for a bipartite pure state |ψ⟩ AB ∈ ℋ AB named unified-(q, s) entanglement (UE) is given as [16] E q,s (|ψ⟩ AB ) = S q,s (ρ A )…”

Section: Preliminaries For Unified Entropy Monogamy Relationsmentioning

confidence: 99%

Unified entropy entanglement with tighter constraints on multipartite systems

Sun¹,

Li²,

Jin³

et al. 2023

Chinese Phys. B

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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 $\alpha$-th power of unified-$(q,s)$ entanglement for $\alpha\geq 1$ and a class of polygamy inequalities in terms of the $\beta$-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's 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.

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