In this study, the entanglement entropy of \textbf{atomic nuclei }has been \textbf{calculated} to investigate the quantum phase transition (QPT) within the framework of the sdg-Interacting Boson Model (sdg-IBM). The entanglement entropy between $ s $-boson with $ d $ and $ g$-bosons ($- bosons$) is used as a signature of the QPTs and applied as a reliable observable for the theoretical study of ${^{108-116}_{48}Cd} $ isotopes. The entanglement entropy effectively characterizes the QPT in the $U_{dg}(14) \leftrightarrow SO_{sdg}(15)$ transition region.} Results show that the increase in entanglement entropy values along the Cadmium isotopic chain indicates mixing symmetry, such that with increasing neutron number, the rotational behavior ($SO_{sdg}(15) limit) becomes more evident.
