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