Information Flow in H → ZZ* → 4l: Spin-Qutrit Tomography of a Real CP-Even a2 Deformation

Quantum entanglement between massive Z bosons produced in Higgs-boson decays has recently become experimentally accessible at the Large Hadron Collider. In H → ZZ(*) → 4l, the two spin-1 Z bosons form an entangled spin-qutrit system whose polarization and spin-correlation structure can be reconstructed from the four-lepton final state. Recent ATLAS and preliminary CMS studies make the spin-density matrix experimentally accessible. For the established LO scalar family we derive the kinematic-mixture identity D = −C_{2,2,2,−2}² Var_q(β) ≤ 0 and the physical chord bound implied by β ≥ 1. We then quantify where information on one specific real CP-even deformation, r = a2/a1, resides in a signal-only LO model. At N = 4500, the two real ATLAS entanglement-sensitive coefficients carry I_r = 3.24. The single-Z polarization moments carry 70.93, all pair-correlation moments 5.34, and the full inclusive angular likelihood 80.40. The coupling-dependent virtuality-bin populations carry 107.09, the continuous mass spectrum 137.26, and the angular distribution conditioned on the masses 71.85; the joint normalized mass–angular likelihood gives 209.32, corresponding to σ(r) = 0.069. An ATLAS-effective N ≈ 2400 benchmark gives 0.095. Thus the entanglement-correlation observables are statistically inefficient for this real a2 direction, whereas the single-boson polarization and virtuality sectors carry most of the information. The per-bin normal coordinate D_k remains unresolvable, with |D_k|/σ(D_k) < 0.07. These results do not characterize other CP-even operators or arbitrary nonlinear density-matrix observables, and they are not a detector-level ATLAS/CMS projection.