Equation 103 · Part 3 · The Bit Comes Back Before the Bearing

Symbol f_1

F_Q(t) \;\approx\; f_1\,\frac{t}{\beta}, \qquad t_G(\delta) \;\approx\; \frac{\beta}{f_1\,\delta^2}.

f_1

What this part means

the per-probe fisher information.

Its job in the formula

$f_1$ occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol f_1Article meaning

Where the article explains it

This is the standard-quantum-limit regime of parameter estimation: for N independent, identically prepared probes each with per-probe Fisher information $f_1$ , the achievable variance scales as 1/(N $f_1$ ) , in contrast to the quadratically better Heisenberg scaling available only when probes are used coherently together [ 13 ] .

The passage around this formula

…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 with per-probe Fisher information $f_1$ , the achievable variance scales as 1/(N $f_1$ ) , in contrast to the quadratically better Heisenberg scaling available only when probes are used coherently together [ 13 ] . Modeling the collected radiation up to time t as contributing $N_\gamma(t)$ $\sim$ t/ $\beta$ roughly independent quanta gives, as…

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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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