Support-Projected Petz Monotone Geometry of Pure Two-Qubit Families: Universal Three-Channel Decomposition and Non-Reduction of Curvature Invariants

We develop a support-projected Petz monotone geometry for pure two-qubit families, obtained by pulling back arbitrary Petz monotone quantum metrics to circuit-defined submanifolds and projecting onto the active spectral support of the associated quantum Fisher information tensor. This framework strictly generalizes the symmetric logarithmic derivative (SLD/Bures) case and includes, as special examples, the Wigner--Yanase and Bogoliubov--Kubo--Mori metrics among many others.