Scattering in scalar models with two Higgs doublets is analyzed as a four-qubit system in the subspaces of weak isospin and flavor. The analysis principle is the commutativity of the initial state density matrix with the transition matrix at leading order in perturbation theory; this condition minimizes entanglement and preserves non-stabilizerness (magic). A consistent set of conditions is obtained, which for an arbitrary initial state imposes SO(8) symmetry on the quartic part of the potential. If, however, the initial state has a definite isospin, the symmetry reduces to SU(2)_R — due to Bose symmetry, which creates entanglement between isospin and flavor. The results demonstrate how quantum information constraints can dictate fundamental symmetries of interactions.
Two dancers, each moving on their own, create a simple and symmetrical dance. But once they start adapting to each other, the movements become more complex, and the original structure is lost. Particles behave similarly in collisions: their intrinsic properties are usually highly entangled, hiding an elegant order. Scientists have discovered that if you remove this entanglement, the system reveals a grand SO(8) symmetry. In this symmetry, there are 28 independent ways to "rotate" a particle without changing its physical properties—whereas in the ordinary world, rotation has only three axes. It’s as if our dance, instead of three dimensions, suddenly acquired 28, yet remained harmonious. Just as spectroscopy breaks light down into pure colors, quantum information methods allow us to separate the entangled states of particles and see each one’s hidden dance. In the Standard Model, which describes fundamental particles, such symmetries are already used, but before we only saw a tangled ball, not a neat pattern. By limiting entanglements, it’s like turning off the noise and enjoying nature’s perfect choreography.
🎯 The SO(8) symmetry has 28 generators — that's like 28 different dance moves you can perform simultaneously, and the dance remains unchanged. In familiar rotation, we have only three such moves.