What does this equation mean?

The covariance equation from the previous section is the formal cost of that fact. Because V commutes with the group action, the radiation’s reduced state along the true heading is a rotated copy of the same state at heading zero, $\rho_{\mathrm{rad}}(g) = U_{\mathrm{rad}}(g)\,\rho_{\mathrm{rad}}(0)\,U_{\mathrm{rad}}(g)^\dagger$. which is a genuine constraint, not a simplifying choice: $F_Q$[$\rho_{\mathrm{rad}}(g)$] is therefore identical at every point along this orbit, since the quantum Fisher information depends only on the local geometry of the state family under the generator, and a rotated copy of the same family has the same local geometry everywhere. $t_G(\delta)$ does not depend on which heading is being estimated. That is the covariance check this construction owes the reader, and it holds by the same argument that makes the Fisher information of a phase-estimation problem independent of the true phase in ordinary quantum metrology.