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In this study, we delve into the observational implications of rotating LoopQuantum Black Holes (LQBHs) within an astrophysical framework. We employsemi-analytical General Relativistic Radiative Transfer (GRRT) computations tostudy the emission from the accretion flow around LQBHs. Our findings indicatethat the increase of Loop Quantum Gravity (LQG) effects results in anenlargement of the rings from LQBHs, thereby causing a more circularpolarization pattern in the shadow images. We make comparisons with the EventHorizon Telescope (EHT) observations of Sgr\,A$^*$ and M\,87$^*$, which enableus to determine an upper limit for the polymetric function $P$ in LQG. Theupper limit for Sgr\,A$^*$ is $0.2$, while for M\,87$^*$ it is $0.07$. Bothblack holes exhibit a preference for a relatively high spin ($a\gtrsim0.5$ forSgr\,A$^*$ and $0.5\lesssim a \lesssim 0.7$ for M\,87$^*$). The constraints forSgr\,A$^*$ are based on black hole spin and ring diameter, whereas forM\,87$^*$, the constraints are further tightened by the polarimetric pattern.In essence, our simulations provide observational constraints on the effect ofLQG in supermassive black holes (SMBH), providing the most consistentcomparison with observation.

Shadows of Loop Quantum Black Holes: Semi-analytical Simulations of Loop Quantum Gravity Effects on Sagittarius A* and M 87*