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Equation 42 · Part 7 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol epsilon

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].
ϵ\epsilon

What this part means

epsilon 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

epsilon 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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