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We derive criterion in the form of inequality based on quantum Fisherinformation and quantum variance to detect multipartite entanglement. It can beregarded as complementary of the well-established PPT criterion in the sensethat it can also detect bound entangled states. The inequality is motivated byY.Akbari-Kourbolagh $et\ al.$[Phys. Rev A. 99, 012304 (2019)] which introduceda multipartite entanglement criterion based on quantum Fisher information. Ourcriterion is experimentally measurable for detecting any $N$-qudit pure statemixed with white noisy. We take several examples to illustrate that ourcriterion has good performance for detecting certain entangled states.

A sufficient Entanglement Criterion Based On Quantum Fisher Information and Variance