Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case

Regula, Bartosz; Martino, Sara Di; Lee, Soojoon; Adesso, Gerardo

doi:10.1103/physrevlett.113.110501

Cited by 83 publications

(54 citation statements)

References 41 publications

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“…Together with the entanglement monogamy relation 13, 14 (see also refs 15–18) this strongly suggests the emergence of multipartite entanglement 19, 20 (triples and quadruples etc. ), which will be studied in the following section (see the results in Fig.…”

Section: Introductionmentioning

confidence: 76%

Avalanche of entanglement and correlations at quantum phase transitions

Krutitsky

Osterloh

Schützhold

2017

Sci Rep

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We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling J and find a sequential increase of entanglement depth d with growing J. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for J = ∞, arriving at a pure L-partite (GHZ type) entanglement of all L spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small J. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should be taken into account in the approximations starting from a mean-field limit.

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Section: Introductionmentioning

confidence: 76%

Avalanche of entanglement and correlations at quantum phase transitions

Krutitsky

Osterloh

Schützhold

2017

Sci Rep

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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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“…proved the squared concurrence follows a general monogamy inequality for the N -qubit system 1 . Monogamy inequalities for different entanglement measures have been noted, such as concurrence 9–12 , entanglement of formation 13, 14 , negativity 15–19 , Rényi entropy entanglement 20, 21 , and Tsallis entropy entanglement 22–24 . For the other physical resources, such as discord and steering, the monogamy property of them has also been discussed 25–28 .…”

Section: Introductionmentioning

confidence: 99%

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

Luo

Zhang

2017

Sci Rep

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We investigate the entanglement distribution in multi-particle systems in terms of unified (q, s)-entropy. We find that for any tripartite mixed state, the unified (q, s)-entropy entanglement of assistance follows a polygamy relation. This polygamy relation also holds in multi-particle systems. Furthermore, a generalized monogamy relation is provided for unified (q, s)-entropy entanglement in the multi-qubit system.

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Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case

Cited by 83 publications

References 41 publications

Avalanche of entanglement and correlations at quantum phase transitions

Avalanche of entanglement and correlations at quantum phase transitions

Entanglement polygon inequality in qubit systems

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

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