  We study information-theoretic properties of scalar models containing two
Higgs doublets $\Phi_a$, where $a=1,2$ is the flavor quantum number.
Considering the 2-to-2 scattering $\Phi_a \Phi_b \to \Phi_c \Phi_d$ 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 $SO(8)$ symmetry acting on the 8 real
components of the two doublets. The $SO(8)$ symmetry leads to the alignment
limit naturally, giving rise to a Standard-Model-like Higgs boson as a
consequence of entanglement suppression.
