Gravitational lensing by a quantum deformed Schwarzschild black hole

We investigate the weak and strong deflection gravitational lensing by a quantum deformed Schwarzschild black hole and find their observables. These lensing observables are evaluated and the detectability of the quantum deformation is assessed, after assuming the supermassive black holes Sgr A* and M87* respectively in the Galactic Center and at the center of M87 as the lenses. We also intensively compare these findings with those of a renormalization group improved Schwarzschild black hole and an asymptotically safe black hole. We find that, among these black holes, it is most likely to test the quantum deformed Schwarzschild black hole via its weak deflection lensing observables in the foreseen future.