<p>We investigate the impact of a small deformation of the electromagnetic Lagrangian on the entanglement properties of photonic quantum states. Using the von Neumann entropy as a quantitative measure, we analyze how such deformations modify reduced density matrices of entangled photons. For two-photon polarization states, we show that maximally entangled states exhibit a universal quadratic reduction of entropy with respect to the deformation parameter, reflecting the fact that maximal entanglement is a local maximum of the entropy. We extend the analysis to multi-photon systems and find that GHZ states display a quadratic scaling of entropy reduction with subsystem size, indicating pronounced fragility, whereas W-type multipartite photonic entangled states exhibit linear scaling, reflecting greater robustness under deformation. We further clarify that normalization factors in reduced density matrices arise from sums of squared amplitudes rather than products, as a direct consequence of the orthogonality of the superposed components. When the deformation parameter is allowed to acquire scale dependence, as expected in effective field-theoretic extensions, the entanglement entropy inherits a corresponding dependence on photon frequency. These results establish a direct connection between field-theoretic modifications of the electromagnetic Lagrangian and quantum entanglement in photonic systems, and suggest that precision measurements of entanglement may serve as sensitive probes of weak nonlinearities in electromagnetic dynamics.</p>