Symbol g

The passage around this formula

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…

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