Entanglement suppression, enhanced symmetry, and a standard-model-like Higgs boson

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 $SO\left(8\right)$ symmetry acting on the eight real components of the two doublets. The $SO\left(8\right)$ symmetry leads to the alignment limit naturally, giving rise to a Standard-Model-like Higgs boson as a consequence of entanglement suppression.