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

Certification of genuine quantum steering is crucial for the verification of an untrusted node in quantum networks. Yadin, Fadel and Gessner (YFG) have shown how a violation of the Cramér-Rao bound hints the presence of quantum steering in the probe state. We recently extended the YFG method to the noisy and non-asymptotic regime. However, in such a scenario, the prior distribution encoding our prior information on the target parameter plays a fundamental role; therefore a prior distribution as reliable as possible is highly recommended. In this work we investigate the role of prior information in the parameter estimation and the certification of quantum steering via a quantum optics experiment with polarization encoding.