Entanglement criterion for multipartite systems based on quantum Fisher information

We propose a sufficient entanglement criterion for the multipartite systems based on quantum Fisher information. It complements the well-established positive partial transpose criterion in the sense that it is also able to detect bound entangled states. Moreover, it improves the well-known upper bound on the quantum Fisher information of separable multiqudit states introduced by Toth et al. [G. Toth and T. Vertesi, Phys. Rev. Lett. 120, 020506 (2018)] and hence detects a greater number of metrologically useful entangled states. This criterion is formulated as a simple inequality which must be fulfilled by the quantum Fisher information of separable states of multipartite systems. Violation of this inequality by a state reveals its entanglement and accordingly confirms its usefulness for quantum metrology. The efficiency of this criterion for detection of entanglement is illustrated through some examples.