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Equation 42 · Part 11 · A Reference Frame Becomes Classical by Publishing Its Orientation

≤

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].
≤

What this part means

Less than or equal to.

Its job in the formula

Less than or equal to.

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

An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.

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Sources cited in the article section

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