We show that the Quantum Fisher Information in quantum metrology, which can be bounded from below in experiments, provides a lower bound on the Average Size of Entangled Subsystems. This is a particular case of a new kind of multipartite entanglement criterion, restricting the relative weights of the pure states of different average sizes of entangled subsystems in the mixed state. We illustrate the strength of this convex criterion and compare it to the original metrological entanglement criterion given by the Entanglement Depth.

Related publications:

• Szalay Sz.  Tóth G., Alternatives of entanglement depth and metrological entanglement criteria, Quantum 9, Paper: 1718 , 50 p. (2025)
• Szalay Sz., k-stretchability of entanglement and the duality of k-separability and k-producibility, Quantum 3, Paper: 204 , 25 p. (2019)

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