Entanglement monogamy relations of qubit systems

Zhu, Xue‐Na; Fei, Shao-Ming

doi:10.1103/physreva.90.024304

Cited by 137 publications

(205 citation statements)

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“…However, there exists a kind of three-qubit mixed states which is entangled but without two-qubit concurrence and three-tangle [38], and the similar case also exists in Nqubit systems [39]. Recently, it was indicated that the squared entanglement of formation (SEF) [3] obeys the monogamy relation in multiqubit systems [40][41][42][43][44][45]. In particular, it was which overcomes the flaw of the MoE of SC and can be utilized to detect all multiqubit entanglement.…”

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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“…Unfortunately, EOF itself does not satisfy the usual monogamy rela- * Electronic address: ykbai@semi.ac.cn † Electronic address: zwang@hku.hk tion even for three-qubit pure states. Recently, it was indicated that the squared entanglement of formation (SEF) obeys the monogamy relation in multiqubit systems [30][31][32][33]. In particular, we proved analytically that the SEF is monogamous in an arbitrary N -qubit mixed state and obeys the relation [32] …”

Section: Introductionmentioning

confidence: 84%

Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems

Bai

Wang

2014

Phys. Rev. A

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We show exactly that the squared entanglement of formation (SEF) obeys a set of hierarchical monogamy relations for an arbitrary N -qubit mixed state. Based on this set of monogamy relations, we are able to construct the set of hierarchical multipartite entanglement indicators for N -qubit states, which still work well even when the concurrence-based indicators lose efficacy. As a by-product, an intriguing analytical relation between the entanglement of formation (EOF) and squared concurrence (SC) for an arbitrary mixed state of 2 ⊗ d systems is derived, making the concurrence calculable via the corresponding EOF. Furthermore, we analyze the multipartite entanglement dynamics in composite cavity-reservoir systems with the present set of hierarchical indicators. Moreover, for multilevel systems, it is illustrated that the SEF can be monogamous even if the SC is polygamous.

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“…Monogamy relations are not always satisfied by entanglement measures. Although the concurrence and entanglement of formation do not satisfy such monogamy inequality, it has been shown that the αth (α ≥ 2) power of concurrence and αth (α ≥ √ 2) power entanglement of formation for N -qubit states do satisfy the monogamy relations [8].In this paper, we study the general monogamy inequalities satisfied by the concurrence and concurrence of assistance. We show that the concurrence of multi-qubit pure states satisfies some generalized monogamy inequalities.…”

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confidence: 95%

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Generalized monogamy relations of concurrence forN-qubit systems

Zhu

Fei

2015

Phys. Rev. A

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We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For N -qubit systems ABC1...CN−2, the monogamy relations satisfied by the concurrence of N -qubit pure states under the partition AB and C1...CN−2, as well as under the partition ABC1 and C2...CN−2 are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.PACS numbers: 03.67.Mn,03.65.UdQuantum entanglement [1][2][3][4][5][6] is an essential feature of quantum mechanics, which distinguishes the quantum from classical world. As one of the fundamental differences between quantum entanglement and classical correlations, a key property of entanglement is that a quantum system entangled with one of other systems limits its entanglement with the remaining others. In multipartite quantum systems, there can be several inequivalent types entanglement among the subsystems and the amount of entanglement with different types might not be directly comparable to each other. The monogamy relation of entanglement is a way to characterize the different types of entanglement distribution. The monogamy relations give rise to the structures of entanglement in the multipartite setting. Monogamy is also an essential feature allowing for security in quantum key distribution [7]. Monogamy relations are not always satisfied by entanglement measures. Although the concurrence and entanglement of formation do not satisfy such monogamy inequality, it has been shown that the αth (α ≥ 2) power of concurrence and αth (α ≥ √ 2) power entanglement of formation for N -qubit states do satisfy the monogamy relations [8].In this paper, we study the general monogamy inequalities satisfied by the concurrence and concurrence of assistance. We show that the concurrence of multi-qubit pure states satisfies some generalized monogamy inequalities.The concurrence for a bipartite pure state |ψ AB is given by [10][11][12] where ρ A is the reduced density matrix by tracing over the subsystem B, ρ A = T r B (|ψ AB ψ|). The concurrence is extended to mixed states ρ = i p i |ψ i ψ i |, 0 ≤ p i ≤ 1, i p i = 1, by the convex roof extension,where the minimum is taken over all possible pure state decompositions of ρ AB . For a tripartite state |ψ ABC , the concurrence of assistance is defined by [13] C a (|ψ ABC ) ≡ C a (ρ AB ) = max {pi,|ψi } ifor all possible ensemble realizations of ρ AB = T r C (|ψ ABC ψ|) = i p i |ψ i AB ψ i |. When ρ AB = |ψ AB ψ| is a pure state, then one has C(|ψ AB

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Entanglement monogamy relations of qubit systems

Cited by 137 publications

References 29 publications

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

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

Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems

Generalized monogamy relations of concurrence forN-qubit systems

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