← All parts of this equation

Equation 37 · Part 10 · The Bit Comes Back Before the Bearing

Symbol delta^2

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\}.
δ2\delta^2

What this part means

the square of delta; the alignment tolerance the observer has decided to demand, also in radians, and tG(δ)t_G(\delta) has units of time [ 12 ].

Its job in the formula

delta2a^2 appears in the objective or constraint used by the optimization on the right.

Where the article explains it

δ\delta is the alignment tolerance the observer has decided to demand, also in radians, and tG(δ)t_G(\delta) has units of time [ 12 ] .

The passage around this formula

For the 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} , i.e. inverse radians squared, and since g is already dimensionless, FQF_Q is a pure number. δ\delta is the alignment tolerance the observer has decided to demand, also in…

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers 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.