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arXiv:2203.14183 · Quantum Information Processing

Detection of genuine tripartite entanglement based on Bloch representation of density matrices

Hui Zhao, Yu-Qiu Liu, Naihuan Jing, Zhi‐Xi Wang, Shao-Ming Fei

Published Mar 1, 2022• 6 citations
arXivHTMLPDF
DOI
10.1007/s11128-022-03456-2

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Abstract We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.
In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies.