We study information-theoretic properties of scalar models containing two Higgs doublets $Φ_𝑎$, where $𝑎=1$, 2 is the flavor quantum number. Considering the 2-to-2 scattering $Φ_𝑎⁢Φ_𝑏→Φ_𝑐⁢Φ_𝑑$ as a two-qubit system in the flavor subspace and the 𝑆-matrix as a quantum logic gate, we analyze the entanglement power of the 𝑆-matrix at the tree level, in the limit the gauge coupling is turned off. Demanding the suppression of flavor entanglement during the scattering, the perturbative 𝑆-matrix in the broken phase can only be in the equivalent class of the Identity gate and the scalar potential exhibits a maximally enhanced 𝑆⁢𝑂⁡(8) symmetry acting on the eight real components of the two doublets. The 𝑆⁢𝑂⁡(8) symmetry leads to the alignment limit naturally, giving rise to a Standard-Model-like Higgs boson as a consequence of entanglement suppression.