  Decoherence, resulting from unwanted interaction between a qubit and its
environment, poses a serious challenge towards the development of quantum
technologies. Recently, researchers have started analysing how real-time
Hamiltonian learning approaches, based on estimating the qubit state faster
than the environmental fluctuations, can be used to counteract decoherence. In
this work, we investigate how the back-action of the quantum measurements used
in the learning process can be harnessed to extend qubit coherence. We propose
an adaptive protocol that, by learning the qubit environment, narrows down the
distribution of possible environment states. While the outcomes of quantum
measurements are random, we show that real-time adaptation of measurement
settings (based on previous outcomes) allows a deterministic decrease of the
width of the bath distribution, and hence an increase of the qubit coherence.
We numerically simulate the performance of the protocol for the electronic spin
of a nitrogen-vacancy centre in diamond subject to a dilute bath of $^{13}$C
nuclear spin, finding a considerable improvement over the performance of
non-adaptive strategies.
