  A universal approach to decoherence control combined with quantum estimation
theory reveals a critical behavior, akin to a phase transition, of the
information obtainable by a qubit probe concerning the memory time of
environmental fluctuations. This criticality emerges only when the probe is
subject to dynamical control. It gives rise to a sharp transition between two
dynamical phases characterized by either a short or long memory time compared
to the probing time. This phase-transition of the environmental information is
a fundamental feature that facilitates the attainment of the highest estimation
precision of the environment memory-time and the characterization of probe
dynamics.
