  We present a thorough observational investigation of the heuristic quantised
ringdown model presented in Foit & Kleban (2019). This model is based on the
Bekenstein-Mukhanov conjecture, stating that the area of a black hole horizon
is an integer multiple of the Planck area $l_P^2$ multiplied by a
phenomenological constant, $\alpha$, which can be viewed as an additional black
hole intrinsic parameter. Our approach is based on a time-domain analysis of
the gravitational wave signals produced by the ringdown phase of binary black
hole mergers detected by the LIGO and Virgo collaboration. Employing a full
Bayesian formalism and taking into account the complete correlation structure
among the black hole parameters, we show that the value of $\alpha$ cannot be
constrained using only GW150914, in contrast to what was suggested in Foit &
Kleban (2019). We proceed to repeat the same analysis on the new gravitational
wave events detected by the LIGO and Virgo Collaboration up to 1 October 2019,
obtaining a combined-event measure equal to $\alpha = 15.6^{+20.5}_{-13.3}$ and
a combined log odds ratio of $0.1 \pm 0.6$, implying that current data are not
informative enough to favour or discard this model against general relativity.
We then show that using a population of $\mathcal{O}(20)$ GW150914-like
simulated events - detected by the current infrastructure of ground-based
detectors at their design sensitivity - it is possible to confidently falsify
the quantised model or prove its validity, in which case probing $\alpha$ at
the few % level. Finally we classify the stealth biases that may show up in a
population study.
