Remark: Quantum-information comparison

The input family has symmetric logarithmic derivative, on its support,

and therefore input quantum Fisher information

The preceding proof establishes the post-step measurement bound directly. Its relation to the standard optimization of classical Fisher information over measurements is consistent with the Braunstein–Caves framework BraunsteinCaves1994. No equality of $F_A$, $F_C$, and the post-step quantum Fisher information is asserted.