Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

Kim, Jeong San; Das, Ajoy Kumar; Sanders, Barry C.

doi:10.1103/physreva.79.012329

Cited by 166 publications

(129 citation statements)

References 28 publications

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“…where E a is the corresponding entanglement measure of assistance associated to E. Such polygamy inequality has been deeply investigated in recent years, and was generalized to multiqubit systems and classes of higherdimensional quantum systems [12,[14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Tighter Constraints of Multiqubit Entanglement*

Yang

Chen²,

Fei

et al. 2019

Commun. Theor. Phys.

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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-q entanglement and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.the squared convex-roof extended negativity (CREN) N 2 c [12, 13] satisfy the monogamy relations for multiqubit states.

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Section: Introductionmentioning

confidence: 99%

Tighter Constraints of Multiqubit Entanglement*

Yang

Chen²,

Fei

et al. 2019

Commun. Theor. Phys.

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“…One of the most important issues closely related to entanglement measure is the monogamy relation of entanglement [23], which states that, unlike classical correlations, if two parties A and B are maximally entangled, then neither of them can share entanglement with a third party C. An important question in this field is to determine whether a given entanglement measure is monogamous. Considerable efforts have been devoted to this task in the last two decades [19,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] ever since Coffman, Kundu, and Wootters (CKW) presented the first quantitative monogamy relation in Ref. [19] for threequbit states.…”

mentioning

confidence: 99%

Multipartite entanglement measure and complete monogamy relation

Guo

Zhang

2020

Phys. Rev. A

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Although many different entanglement measures have been proposed so far, much less is known in the multipartite case, which leads to the previous monogamy relations in literatures are not complete. We establish here a strict framework for defining multipartite entanglement measure (MEM): apart from the postulates of bipartite measure [i.e., vanishing on separable and nonincreasing under local operations and classical communication (LOCC)], a genuine MEM should additionally satisfy the unification condition and the hierarchy condition. We then come up with a complete monogamy formula under the unified MEM (an MEM is called a unified MEM if it satisfies the unification condition). Consequently, we propose MEMs which are multipartite extensions of entanglement of formation (EoF), concurrence, tangle, the convex-roof extension of negativity and negativity, respectively. We show that multipartite extensions of the bipartite measures that are defined by the convex-roof structure are completely monogamous, the extensions of EoF, concurrence and tangle are genuine MEMs (an MEM is called a genuine MEM if it satisfies both the unification condition and the hierarchy condition), and multipartite extensions of both negativity and the convex-roof extension of negativity are unified MEMs but not genuine MEMs. PACS numbers: 03.67.Mn, 03.65.Db, 03.65.Ud.Introduction.-Entanglement is recognized as the most important resource in quantum information processing tasks [1]. A fundamental problem in this field is to quantify entanglement. Many entanglement measures have been proposed for this purpose, such as the distillable entanglement [2], entanglement cost [2, 3], entanglement of formation [3, 4], concurrence [5][6][7], tangle [8], relative entropy of entanglement [9,10], negativity [11,12], geometric measure [13][14][15], squashed entanglement [16,17], the conditional entanglement of mutual information [18], three-tangle [19], the generalizations of concurrence [20,21], and the α-entanglement entropy [22], etc. However, apart from the α-entanglement entropy, all other measures are either only defined on the bipartite case or just discussed with only the axioms of the bipartite case.

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“…CREN is equivalent to concurrence for any pure state with Schmidt rank 2 [38]. Consequently for any twoqubit mixed state ρ AB , one has N c (ρ AB ) = C(ρ AB ) (21) and N a (ρ AB ) = C a (ρ AB ).…”

Section: Tighter Generalized Monogamy and Polygamy Relations Of Negatmentioning

confidence: 99%

Tighter generalized monogamy and polygamy relations for multiqubit systems

Jin

Fei

2019

Quantum Inf Process

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We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the αth (0 ≤ α ≤ 2) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the αth (0 ≤ α ≤ 2) power of concurrence for N -qubit pure states under the partition AB and C1...CN−2, as well as under the partition ABC1 and C2 · · · CN−2. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity.PACS numbers:

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Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

Cited by 166 publications

References 28 publications

Tighter Constraints of Multiqubit Entanglement*

Tighter Constraints of Multiqubit Entanglement*

Multipartite entanglement measure and complete monogamy relation

Tighter generalized monogamy and polygamy relations for multiqubit systems

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