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Equation 103 · Part 10 · The Bit Comes Back Before the Bearing

subscript

FQ(t)  ≈  f1 tβ,tG(δ)  ≈  βf1 δ2.F_Q(t) \;\approx\; f_1\,\frac{t}{\beta}, \qquad t_G(\delta) \;\approx\; \frac{\beta}{f_1\,\delta^2}.
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

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 that adds like an independent sample rather than like a decoded codeword. This is the standard-quantum-limit regime of parameter estimation: for N independent, identically prepared probes each…

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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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