Equation 52 · The Bit Comes Back Before the Bearing

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F_Q[\rho_{\mathrm{rad}}(g)]

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F_Q

Symbol F_Q

$F_Q$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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\rho_{\mathrm{rad}}

Symbol rho_rad

rh $o_r$ ad is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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g

Symbol g

g is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subscript

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What the article says around this equation

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.

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