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Advanced Quantum Technologies

A Note On Entanglement Detection via the Generalized Realignment Moments

Xiaofen Huang, Xishun Zhu, Bin Chen, Naihuan Jing, Shao‐Ming Fei

Published Jan 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT The experimental detection of quantum entanglement is of great importance in quantum information processing. We present two separability criteria based on the generalized realignment moments. By incorporating additional parameters, these criteria prove to be more flexible and stronger than some of the existing ones. Detailed examples are given to demonstrate their availability and feasibility for entanglement detection.

DOI
10.1002/qute.202500794

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ABSTRACT The experimental detection of quantum entanglement is of great importance in quantum information processing. We present two separability criteria based on the generalized realignment moments. By incorporating additional parameters, these criteria prove to be more flexible and stronger than some of the existing ones. Detailed examples are given to demonstrate their availability and feasibility for entanglement detection.
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The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability criteria. The proposed separability criteria can detect more entanglement than the previous separability criteria. Moreover, we provide new criteria for detecting the genuine tripartite entanglement and lower bounds for the concurrence and convex-roof extended negativity. The advantages of results are demonstrated through detailed examples.
The detection and quantification of quantum entanglement are central problems in quantum information science. Based on the realignment of density matrices and the vectorization of reduced density matrices, we construct a family of enhanced separability criteria for bipartite and multipartite quantum systems. Our criteria recover the previously proposed realignment-based criteria as special cases and detect more entanglement than the earlier ones. Moreover, we derive tighter lower bounds for the concurrence and the convex-roof extended negativity, criteria for detecting the genuine tripartite entanglement, and lower bounds on genuine-multipartite-entanglement concurrence. The advantages of our results are demonstrated with detailed examples.
Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the criterion based on Bloch representations, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analog of permutation separability criteria in the even-partite systems.