Abstract
We study genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of generalized Pauli operators. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra \(\mathfrak {su}(d)\), the Weyl representation with generalized Pauli operators has one uniformed type of generators that simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect genuine entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more genuine entangled states than previous methods as backed by detailed examples.
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All data generated or analysed during this study are available from the corresponding author on reasonable request.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant Nos. 12075159 and 12126351, Simons Foundation under grant no. 523868, Academy for Multidisciplinary Studies, Capital Normal University.
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Zhao, H., Liu, YQ., Jing, N. et al. Detection of genuine entanglement for multipartite quantum states. Quantum Inf Process 21, 315 (2022). https://doi.org/10.1007/s11128-022-03659-7
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DOI: https://doi.org/10.1007/s11128-022-03659-7