Separability criteria based on Bloch representation of density matrices

Zhao, Hui; Zhang, Mei-Ming; Jing, Naihuan

doi:10.1007/s11128-019-2504-2

Cited by 12 publications

(9 citation statements)

References 25 publications

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“…Remark 2: The upper bound of Corollary 1 is the same as in [15] and [25]. And Corollary 1 is the generalization of the results of [14].…”

Section: Upper Bounds Of the Norms Of Bloch Vectorsmentioning

confidence: 82%

“…In [6], the norms of the Bloch vectors give rise to a general framework to detect different classes of GME for arbitrary dimensional quantum systems. Recently, based on the norms of the correlation tensors, Zhao et al [25] have been studied the separability criteria by matrix method and necessary conditions of separability for multipartite systems are given under arbitrary partition.…”

Section: Introductionmentioning

confidence: 99%

“…Remark 3: The upper bounds of Theorem 2 is a generalization of Theorem 2 given in [15] and Theorem 7 given in [25], respectively. Set (20) gives rise to…”

mentioning

confidence: 96%

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Necessary conditions for classifying $$\mathbf {m}$$-separability of multipartite entanglements

Zhu

Zheng

et al. 2020

Quantum Inf Process

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We study the norms of the Bloch vectors for arbitrary n-partite quantum states. A tight upper bound of the norms is derived for n-partite systems with different individual dimensions. These upper bounds are used to deal with the separability problems. Necessary conditions are presented for m-separable states in n-partite quantum systems. Based on the upper bounds, classification of multipartite entanglement is illustrated with detailed examples.

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“…Remark 2: The upper bound of Corollary 1 is the same as in [15] and [25]. And Corollary 1 is the generalization of the results of [14].…”

Section: Upper Bounds Of the Norms Of Bloch Vectorsmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Necessary conditions for classifying $$\mathbf {m}$$-separability of multipartite entanglements

Zhu

Zheng

et al. 2020

Quantum Inf Process

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“…We can get the following corollary: Fig. 1 The function f 1 (x) from Theorem 1 (solid curve line) and f 2 (x) from [18] (solid line).…”

Section: Detection Of Genuine Tripartite Entanglementmentioning

confidence: 88%

Detection of multipartite entanglement based on Heisenberg-Weyl representation of density matrices

Zhao,

Yang,

Jing

et al. 2022

Preprint

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We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria.

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“…separability tests were given by using the Bloch representation [28], by the matrix method [29], by the upper bound of the Bloch vectors [30], and by using witness operators [31]. Detection of genuine tripartite entanglement was given by multiple sequential observers [32], and by local marginals [33].…”

mentioning

confidence: 99%

Improved tests of genuine entanglement for multiqudits

Zhang,

Jing,

Zhao

et al. 2023

EPL

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We give an improved criterion of genuine multipartite entanglement for an important class ofmultipartite quantum states using generalized Bloch representations of the density matrices. The practical criterion is designed based on the Weyl operators and can be used for detecting genuine multipartite entanglement in higher dimensional systems. The test is shown to be significantly stronger thansome of the most recent criteria.

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Separability criteria based on Bloch representation of density matrices

Cited by 12 publications

References 25 publications

Necessary conditions for classifying $$\mathbf {m}$$-separability of multipartite entanglements

Necessary conditions for classifying $$\mathbf {m}$$-separability of multipartite entanglements

Detection of multipartite entanglement based on Heisenberg-Weyl representation of density matrices

Improved tests of genuine entanglement for multiqudits

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