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Equation 96 · Part 1 · The Bit Comes Back Before the Bearing

Symbol F_Q

FQ=4[⟨∂gψ∣∂gψ⟩−∣⟨ψ∣∂gψ⟩∣2]=4ℏ2Var⁡J^,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,
FQF_Q

What this part means

the exact quantum Fisher information.

Its job in the formula

FQF_Q is part of the quantity the equation computes from the expression on the right.

Where the article explains it

For a pure-state family generated by a Hermitian charge, the exact quantum Fisher information is

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 FQ=4[⟨∂gψ∣∂gψ⟩−∣⟨ψ∣∂gψ⟩∣2]=4ℏ2Var⁡J^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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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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