← All parts of this equation

Equation 37 · Part 9 · The Bit Comes Back Before the Bearing

Symbol C_t

Var⁡g^  ≥  1FQ[ρrad(g)],tG(δ)  =  min⁡{ t:Var⁡g^∣R∪Ct≤δ2 }.\operatorname{Var}\hat g \;\ge\; \frac{1}{F_Q\big[\rho_{\mathrm{rad}}(g)\big]}, \qquad t_G(\delta) \;=\; \min\Big\{\,t : \operatorname{Var}\hat g\big|_{R\cup C_t} \le \delta^2\,\Big\}.
CtC_t

What this part means

CtC_t appears in the objective or constraint used by the optimization on the right.

Its job in the formula

CtC_t appears in the objective or constraint used by the optimization on the right.

The passage around this formula

…compass, returned has to mean something else, because g is a continuous parameter and no channel can reproduce an unknown continuous value exactly. The honest promise is metrological: the same agent, using the same R∪\cup CtC_t , applies the best available measurement and estimator g^\hat g , and the achievable mean-squared error is bounded below by the quantum Cramér-Rao bound, Var⁡g^  ≥  1FQ[ρrad(g)],tG(δ)  =  min⁡{ t:Var⁡g^∣R∪Ct≤δ2 }\operatorname{Var}\hat g \;\ge\; \frac{1}{F_Q\big[\rho_{\mathrm{rad}}(g)\big]}, \qquad t_G(\delta) \;=\; \min\Big\{\,t : \operatorname{Var}\hat g\big|_{R\cup C_t} \le \delta^2\,\Big\}. FQF_Q is the quantum Fisher information of the radiation’s reduced state with respect to g ; it carries units of g−2g^{-2} ,…

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.