Equation 42 · Part 13 · A Reference Frame Becomes Classical by Publishing Its Orientation

Starting index or lower bound: G

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

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

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

Full expressionStarting index or lower bound: GArticle meaning

The passage around this formula

For a Haar-uniform prior, define the fragment success probability $p_{\epsilon}(F)= \int_G dg\int_{d(\hat g,g)\leq\epsilon} \operatorname{Tr}\!\left[\rho_F(g)M_F(d\hat g)\right]$ . 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

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

See this notation across published equations →

Sources cited in the article section

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