Detection of Multipartite Entanglement Based on Heisenberg-Weyl Representation of Density Matrices

Zhao, Hui; Yu, Y. B.; Jing, Naihuan; Wang, Zhi‐Xi; Fei, Shao-Ming

doi:10.1007/s10773-022-05123-9

Cited by 4 publications

(3 citation statements)

References 18 publications

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“…Quite recently, Asadian et al introduced a new Hermitian Bloch basis derived from the Heisenberg-Weyl operators [59], the so called Heisenberg-Weyl observable basis, which conveniently combines many desirable properties of the Bloch vector parametrization. Moreover, these Heisenberg-Weyl observables hold distinctive features from those of GGM observables and can be applied to certain quantum information tasks [60][61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Steerability criteria based on Heisenberg–Weyl observables

Lai

Luo

2023

J. Phys. A: Math. Theor.

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Einstein-Podolsky-Rosen (EPR) steering is an intermediate form of nonlocality which interpolates between entanglement and Bell nonlocality. It has been shown that EPR steerable states are fundamental resources for one-sided device-independent quantum information tasks. Nevertheless, distinguishing quantum steerable states from the unsteerable ones in general cases remains a big challenge under active studies. The generalized Bloch representation of density matrices in terms of the Heisenberg observables is a useful tool for analyzing characteristics of quantum systems and plays an important role in quantum information. In this work, the role of this representation in detection of EPR steering is studied. More specifically, based on the correlation matrices of the Heisenberg-Weyl observables, a family of steerability criteria for arbitrary dimensional bipartite systems are proposed. A large class of Hermitian operators, which can conveniently witness steering in some scenarios, are further provided. Finally, these criteria are illustrated through several examples, are compared with some existing ones, and their power and advantages are exhibited in certain cases.

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Section: Introductionmentioning

confidence: 99%

Steerability criteria based on Heisenberg–Weyl observables

Lai

Luo

2023

J. Phys. A: Math. Theor.

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“…Our method further demonstrates that Weyl operators can be widely applied in quantum information realm [ 13 , 14 , 15 ]. Particularly, Weyl operators also play important roles in entanglement detection [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. In fact, Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the separability criteria in terms of the Weyl operators for bipartite and multipartite quantum systems were presented in Ref. [ 17 ]. The Weyl operators also play a crucial role in constructing the Weyl discrete channels.…”

Section: Introductionmentioning

confidence: 99%

Separability Criteria Based on the Weyl Operators

Huang

Zhang

Zhao

et al. 2022

Entropy

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Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.

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