Quantum sensing is one of the most promising applications of near-term quantum systems. In this talk, I will introduce a new form of exponential entanglement advantage in the context of sensing correlated noise. Specifically, we focus on the problem of estimating parameters associated with Lindblad dephasing dynamics and show that entanglement can lead to an exponential enhancement in the sensitivity (as quantified via quantum Fisher information of the sensor state), for estimating a small parameter characterizing the deviation of system Lindbladian from a class of maximally correlated dephasing dynamics. This result stands in stark contrast with previously studied scenarios of sensing uncorrelated dephasing noise, where one can prove that entanglement does not lead to an advantage in the signal-to-noise ratio. Our work thus opens a novel pathway towards achieving entanglement-based sensing advantage, which may find applications in characterizing decoherence dynamics of current quantum devices. Further, our approach provides a potential quantum-enhanced probe of many-body correlated phases by measuring fluctuations generated by a sensing target. I will also discuss the realization of our protocol using near-term quantum hardware.