Experimental activation of hidden metrological steerability in quantum channels via stochastic filtering
Quantum steering-assisted metrology allows a trusted party (Bob) to improve local phase estimation by exploiting classical information communicated by an untrusted party (Alice). In realistic scenarios, however, the channel is subject to noise that degrades steerability and suppresses the associated metrological advantage. Here, we demonstrate that stochastic pre- and post-filtering operations can revive the violation of the metrological steering inequality (MSI) in phase-covariant amplitude-damping channels where it is initially absent, thereby activating a hidden metrological steerability and restoring their usefulness for quantum metrology. Specifically, the critical damping parameter beyond which the MSI violation is suppressed is raised from $γ_c \approx 0.5$ to $γ_c \approx 0.75$ for the largest filter strength considered. We verify this in a photonic experiment, where polarization qubits carrying the encoded phase are transmitted through an amplitude-damping channel implemented with a two-path Sagnac interferometer, and the stochastic operations are realized with glass plates at the Brewster angle. By tuning the filter strength and scanning the damping parameter over its full range, we observe the revival of the MSI violation, obtained at the cost of a reduced success probability inherent to the stochastic nature of the filtering operations. Our results establish that metrological utility and steerability can be activated through stochastic operations even when these properties are absent in the original noisy channel, extending filtering-based activation from witnesses of nonclassicality to a certified and operationally quantified metrological advantage.