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Laser Physics Letters

Parameterized multipartite entanglement based on principal basis matrix representations

Shu-Ying Zhuang, Hui Zhao, Tao Li

Published Jul 1, 2025• 0 citations
Publisher

Abstract

Abstract We study entanglement in arbitrary multipartite quantum systems by using principal basis matrix representations. Compared to the usual Bloch representation of a density matrix using three types of generators, the principal basis matrix representation can simplify computation due to its uniform type of generator. We take advantage of this simplicity to derive parameterized multipartite entanglement criteria. By constructing the parameterized matrices using the correlation tensors, we first present criteria for detecting tripartite entangled states under bipartition and full partition. Then, we generalize these results to obtain parameterized criteria for detecting arbitrary multipartite entangled states under the k-partition. Detailed examples show that our methods can detect more entangled states than previous ones.

DOI
10.1088/1612-202x/adf03d

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Based on the realignment moments of density matrix, we study parameterized entanglement criteria for bipartite and multipartite states. By adjusting the different parameter values, our criterion can detect not only bound entangled states, but also non-positive partial transpose entangled states for bipartite quantum systems. Moreover, we propose the definition of multipartite realignment moments and generalize the result of bipartite systems to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. And we further improve the conclusion to obtain another new entanglement criterion. The new method can detect more entangled states than previous methods as backed by detailed examples.
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Abstract Based on the generalized Bloch representation, we study the separability and entanglement of arbitrary dimensional multipartite quantum states. Some sufficient and some necessary criteria are presented. For certain states, these criteria together are both sufficient and necessary. Detailed examples show that our criteria are better than some existing ones in identifying separability. Based on these criteria, the largest separable ball around the maximally mixed state for arbitrary multi-qubit systems is found, and it is proved that its radius defined via the l 1-norm of the Bloch vector is the constant 1. Furthermore, the criteria in this paper can be implemented experimentally.