Entanglement suppression, enhanced symmetry, and a standard-model-like Higgs boson
Marcela Carena, Ian Low, Carlos E. M. Wagner, Ming-Lei Xiao
Abstract
We study information-theoretic properties of scalar models containing two Higgs doublets ${\mathrm{\ensuremath{\Phi}}}_{a}$, where $a=1$, 2 is the flavor quantum number. Considering the 2-to-2 scattering ${\mathrm{\ensuremath{\Phi}}}_{a}{\mathrm{\ensuremath{\Phi}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Phi}}}_{c}{\mathrm{\ensuremath{\Phi}}}_{d}$ 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 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.