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Equation 42 · Part 6 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol hat g

pϵ(F)=∫Gdg∫d(g^,g)≤ϵTr⁡ ⁣[ρF(g)MF(dg^)].p_{\epsilon}(F)= \int_G dg\int_{d(\hat g,g)\leq\epsilon} \operatorname{Tr}\!\left[\rho_F(g)M_F(d\hat g)\right].
g^\hat g

What this part means

hat g appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

Its job in the formula

hat g appears in the bound of this integral. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

For a Haar-uniform prior, define the fragment success probability pϵ(F)=∫Gdg∫d(g^,g)≤ϵTr⁡ ⁣[ρF(g)MF(dg^)]p_{\epsilon}(F)= \int_G dg\int_{d(\hat g,g)\leq\epsilon} \operatorname{Tr}\!\left[\rho_F(g)M_F(d\hat g)\right]. This is again a definition. The Haar measure dg is normalized to one. A frequentist worst-case version could replace the average over g with an infimum; the two must not be mixed after seeing results.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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