General monogamy of Tsallis<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-entropy entanglement in multiqubit systems

Luo, Yu; Tian, Tian; Shao, Lian-He; Li, Yongming

doi:10.1103/physreva.93.062340

Cited by 87 publications

(68 citation statements)

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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.…”

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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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confidence: 99%

Multipartite entanglement measure and complete monogamy relation

Guo

Zhang

2020

Phys. Rev. A

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“…We place the proof of Theorem 15 in Appendix A. Next We remark that from the proof, other entanglement measures in terms of the approach proposed in (3) for the states in two‐qubit systems can be obtained, such as Tsallis‐ q entanglement measure [ 43 ] and R

\overset{e}{true}

nyi‐α entanglement measure [ 44 ] when q [ 45 ] and α [ 46 ] are in some regions.…”

Section: Applicationsmentioning

confidence: 99%

An Extension of Entanglement Measures for Pure States

Shi

Chen

2021

Annalen der Physik

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To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement measure is entanglement monotone and convex are presented, as well as the interpretation of smoothed one‐shot entanglement cost. Next, a difference between the measure under the local operation and classical communication and the separability‐preserving operations is presented. Then, the relation between the convex roof extended method and the way here for the entanglement measures built from the geometric entanglement measure for pure states, as well as the concurrence for pure states in two‐qubit systems are considered. It is also shown that the measure is monogamous for 2⊗2⊗d system.

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“…Coffman, Kundu, and Wootters initiated the focus of distribution from a 'one-togroup' entanglement (between a singled-out qubit and a group of qubits) into all 'one-to-one' entanglements (between the singled-out qubit and each individual qubit in the group) [2]. This led to the discovery of the wellknown entanglement monogamy relation, E E E  + | | | , followed by various N-party extensions [3][4][5][6][7][8][9][10][11][12]. Monogamy relations reveal one aspect of fundamental connections among a particular subset of bi-partite entanglements in a multiparty system.…”

Section: Introductionmentioning

confidence: 99%

Entanglement polygon inequality in qubit systems

Qian¹,

Alonso²,

Eberly³

2018

New J. Phys.

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We prove a set of tight entanglement inequalities for arbitrary N-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.

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General monogamy of Tsallisq-entropy entanglement in multiqubit systems

Cited by 87 publications

References 51 publications

Multipartite entanglement measure and complete monogamy relation

Multipartite entanglement measure and complete monogamy relation

An Extension of Entanglement Measures for Pure States

Entanglement polygon inequality in qubit systems

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