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We use hydrodynamics and radiative transfer simulations to study the 21~cmsignal around a bright QSO at $z \sim 10$. Due to its powerful UV and X-rayradiation, the QSO quickly increases the extent of the fully ionized bubbleproduced by the pre-existing stellar type sources, in addition to partiallyionize and heat the surrounding gas. As expected, a longer QSO lifetime,$t_{\rm QSO}$, results in a 21~cm signal in emission located at increasinglylarger angular radii, $\theta$, and covering a wider range of $\theta$. Similarfeatures can be obtained with a higher galactic emissivity efficiency, $f_{\rmUV}$, so that determining the origin of a large ionized bubble (i.e. QSO vsstars) is not straightforward. Such degeneracy could be reduced by takingadvantage of the finite light traveltime effect, which is expected to affect anHII region produced by a QSO differently from one created by stellar typesources. From an observational point of view, we find that the 21 cm signalaround a QSO at various $t_{\rm QSO}$ could be detected by SKA1-low with a highsignal-noise ratio (S/N). As a reference, for $t_{\rm QSO} = 10\,\rm Myr$, aS/N $\sim 8$ is expected assuming that no pre-heating of the IGM has takenplace due to high-$z$ energetic sources, while it can reach value above 10 incase of pre-heating. Observations of the 21~cm signal from the environment of ahigh-$z$ bright QSO could then be used to set constraints on its lifetime, aswell as to reduce the degeneracy between $f_{\rm UV}$ and $t_{\rm QSO}$.

Observing the redshifted 21 cm signal around a bright QSO at $z\sim 10$