A sufficient entanglement criterion based on quantum fisher information and variance

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We derive criterion in the form of inequality based on quantum Fisher information and quantum variance to detect multipartite entanglement. It can be regarded as complementary of the well-established positive partial transpose criterion in the sense that it can also detect bound entangled states. The inequality is motivated by Y Akbari-Kourbolagh et al [Phys. Rev A. 99, 012304 (2019)], which introduced a multipartite entanglement criterion based on quantum Fisher information. Our criterion is experimentally measurable for detecting any N-qudit pure state mixed with white noisy. We take several examples to illustrate that our criterion has good performance for detecting certain entangled states.