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

We study information-theoretic properties of scalar models containing two Higgs doublets Φₐ, where $a=1$, 2 is the flavor quantum number. Considering the 2-to-2 scattering ΦₐΦb→ΦcΦd 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 eight 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.