Finite-size effects in metrology-assisted certification of quantum steering

Certifying the presence of quantum steering, quantum correlation enabling one user to control the quantum state shared with a distant party with superior ability than allowed by a local hidden state model, is crucial for the verification of quantum channels. Nonetheless, its connection to the metrological power of the quantum state has been recently proved. However, such a direct assessment would demand operating with a large number of repetitions. Moreover, experimental imperfections in the setup require the adaptation of the original test to the multiparameter scenario. In this work we extend the already existent protocol, explicitly accounting for the limited resource scenario, and put it under test in a quantum optics exper- iment. The hidden protagonist of our approach is the prior distribution used throughout the process, therefore we performed the experiment investigating how changes in the prior distribution are reflected in the parameter estimation and the validation test.