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Detection of genuine multipartite entanglement based on uncertainty relations

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Abstract

A multipartite state that is not the convex sum of bipartite product states is said to be a genuine multipartite entangled (GME) state, which offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy n-partite W state when \(n = 3, 4, 5\) and 6 and find that the criterion can detect more noisy W states when n ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of 3-qutrit states. The result is stronger than that based on GME concurrence and Fisher information.

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Acknowledgements

Authors were supported by the NNSF of China (Grant No. 11871089) and the Fundamental Research Funds for the Central Universities (Grant Nos. ZG216S1902 and ZG216S2110).

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  1. LMIB (Beihang University), Ministry of Education, and School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Jun Li & Lin Chen

  2. International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, China

    Lin Chen

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  1. Jun Li
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Correspondence to Jun Li or Lin Chen.

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Li, J., Chen, L. Detection of genuine multipartite entanglement based on uncertainty relations. Quantum Inf Process 20, 220 (2021). https://doi.org/10.1007/s11128-021-03154-5

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