Erratum: Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case [Phys. Rev. Lett.<b>113</b>, 110501 (2014)]

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

doi:10.1103/physrevlett.116.049902

Cited by 31 publications

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“…. , n. The MoE of SC can be used to characterize the entanglement structure in multipartite quantum systems and detect the existence of multiqubit entanglement in dynamical procedures [6][7][8][9][10][11][12][13][14][15][16]. Moreover, there are also many works devoted to the topic of entanglement monogamy [17][18][19][20][21][22][23][24] and similar monogamy relations were also established for Gaussian systems [25][26][27], squashed entanglement [28][29][30], entanglement negativity [31][32][33][34][35] and Rényi-α entanglement [36,37].…”

Section: Introductionmentioning

confidence: 99%

General monogamy relation of multiqubit systems in terms of squared Rényi-αentanglement

et al. 2016

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We prove that the squared Rényi-α entanglement (SRαE), which is the generalization of entanglement of formation (EOF), obeys a general monogamy inequality in an arbitrary N -qubit mixed state. Furthermore, for a class of Rényi-α entanglement, we prove that the monogamy relations of the SRαE have a hierarchical structure when the N -qubit system is divided into k parties. As a byproduct, the analytical relation between the Rényi-α entanglement and the squared concurrence is derived for bipartite 2 ⊗ d systems. Based on the monogamy properties of SRαE, we can construct the corresponding multipartite entanglement indicators which still work well even when the indicators based on the squared concurrence and EOF lose their efficacy. In addition, the monogamy property of the µ-th power of Rényi-α entanglement is analyzed.

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Section: Introductionmentioning

confidence: 99%

General monogamy relation of multiqubit systems in terms of squared Rényi-αentanglement

et al. 2016

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“…(1) was originally proven for arbitrary states of three qubits, adopting the squared concurrence as entanglement measure [25]. Variations of the CKW inequality and generalizations to n parties have been established for a number of entanglement measures in discrete as well as continuous variable systems [20,[27][28][29][30][31][32][33][34][35][36][37][38][39]. In particular, the squashed entanglement [40] and the one-way distillable entanglement fulfill Eq.…”

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confidence: 99%

Should Entanglement Measures be Monogamous or Faithful?

et al. 2016

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"Is entanglement monogamous?" asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett's legacy on quantum information theory. While the answer is affirmative in the qualitative sense, the situation is less clear if monogamy is intended as a quantitative limitation on the distribution of bipartite entanglement in a multipartite system, given some particular measure of entanglement. Here, we formalize what it takes for a bipartite measure of entanglement to obey a general quantitative monogamy relation on all quantum states. We then prove that an important class of entanglement measures fail to be monogamous in this general sense of the term, with monogamy violations becoming generic with increasing dimension. In particular, we show that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entanglement structure of the fully antisymmetric state in arbitrary dimension. Nevertheless, monogamy of such entanglement measures can be recovered if one allows for dimension-dependent relations, as we show explicitly with relevant examples.Introduction. Entanglement is a quintessential manifestation of quantum mechanics [1,2]. The study of entanglement and its distribution reveals fundamental insights into the nature of quantum correlations [3], on the properties of manybody systems [4,5], and on possibilities and limitations for quantum-enhanced technologies [6]. A particularly interesting feature of entanglement is known as monogamy [7], that is, the impossibility of sharing entanglement unconditionally across many subsystems of a composite quantum system.In the clearest manifestation of monogamy, if two parties A and B with the same (finite) Hilbert space dimension are maximally entangled, then their state is a pure state |Φ AB [8], and neither of them can share any correlation-let alone entanglement-with a third party C, as the only physically allowed pure states of the tripartite system ABC are product states |Φ AB ⊗ |Ψ C . Consider now the more realistic case of A and B being in a mixed, partially entangled state ρ AB . It is then conceivable for more parties to get a share of such entanglement. Namely, a state ρ AB on a Hilbert space H A ⊗ H B is termed "n-shareable" with respect to subsystem B if it admits a symmetric n-extension, i.e. a state ρ AB 1 ...B n on H A ⊗ H ⊗n B invariant under permutations of the subsystems B 1 , . . . , B n and such that the marginal state of A and any B j amounts to ρ AB . While even an entangled state can be shareable up to some number of extensions, a seminal result is that a state ρ AB is n-shareable for all n 2 if and only if it is separable, that is, no entangled state can be infinitely-shareable [7,[9][10][11][12]. This statement formalizes exactly the monogamy of entanglement (in an asymptotic setting), and has many important implications, including the equivalence between asymptotic quantum cloning and state e...

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“…Closed formulae for upper bound on three tangles of nine classes of four qubit states [27], are obtained and the results compared with those of ref. [28,29]. Our results offer tighter constraints on three-way entanglement of a given qubit with the rest of the system than those used in ref.…”

Section: Introductionmentioning

confidence: 64%

“…Our results offer tighter constraints on total three-way entanglement of a given qubit with the rest of the system than those used in ref. [28,29] to verify monogamy of four-qubit quantum entanglement. …”

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confidence: 99%