subtraction

The passage around this formula

The compass’s Fisher information does not have an analogous reason to jump. For a pure-state family generated by a Hermitian charge, the exact quantum Fisher information is $F_Q = 4\Big[\langle\partial_g\psi|\partial_g\psi\rangle - |\langle\psi|\partial_g\psi\rangle|^2\Big] = \frac{4}{\hbar^2}\operatorname{Var}\hat J$. a standard identity in quantum metrology [ 12 ] . Before scrambling, this is fixed by how the compass itself was built — a large, well-prepared gyroscope has a large charge variance and a small intrinsic uncertainty on its own heading. After scrambling, that fixed total has to be reconstructed piecemeal from radiation, and each individually emitted quantum, to the extent it is only weakly and independently correlated with g once the hole’s own state is traced over, contributes an addition to the total…

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