Abstract: Despite the observation of Gravitational Waves (GWs) in 2015, a proof that Gravity is quantum in nature still eludes us. An unambiguous proof of existence of Quantum Gravity would be the detection of a single graviton, the quantum field that would serve as a carrier of the gravitational interaction, if the latter exists as a fundamental, and not emergent, force of Nature. However this task, despite excellent ideas, some of which are quite recent (e.g. search for the `noise' of squeezed gravitons in interferometers), seems to be very difficult to achieve, or distinguish from the effects of classical GWs, at least within the framework of presently available technologies. Nonetheless, while the direct detection of single gravitons remains beyond experimental reach at present, this may not be the case for squeezed quantum graviton states produced in some collective phenomena. In the talk, I will concentrate on a recent proposal of collaborators and myself, which suggests a method for probing quantum gravitational effects via squeezed gravitons produced through astrophysical processes near rotating black holes. The key novelty lies in the exploitation of condensates (“clouds’’) of massive axion-like particles (ALPs) possibly formed via a superradiance instability in the interaction between the ALP and the rotating black hole. The exponential growth of such condensates offers a macroscopic amplification mechanism of potential quantum-gravity effects, due to the very large numbers of ALPs involved in the cloud. This, in turn, enables the generation of sufficiently large numbers of quantum-entangled multi-mode  squeezed graviton states that could be detectable in current or near-future interferometric data. In the talk, I will explain in detail how spin-polarised-entangled pairs of squeezed gravitons can be produced through interactions of ALPs, studied within the framework of weak-quantum-graviton effective field theories. The non-observation by the LIGO–Virgo–KAGRA  interferometers of such squeezed gravitons at present can place (for the first time) stringent upper-bound constraints on ALP cloud lifetimes.  I will also demonstrate  that the structure of the entangled graviton states (when the latter are expressed in a left-right polarization basis, analogous to EPR states in particle physics) depends highly on whether their production occurs via ALP annihilation (due to conventional General-Relativity-type interactions), or decays of ALPs (due to the presence of gravitationally anomalous Chern-Simons interactions of ALPs with gravity, which are non-trivial in the background of a rotating black hole). I will draw analogies between the above effects and some effects of squeezed photons in quantum optics, but I will also stress important differences. This idea combines four frontiers — black hole physics, axion phenomenology, gravitational waves and quantum gravity — in a compelling and testable framework.