Equation 48 · Part 1 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol pi

[0,\pi]

\pi

What this part means

the values from zero to.

Its job in the formula

pi is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol piArticle meaning

Where the article explains it

$\left(\frac{\operatorname{Tr}(R_1^{\mathsf T}R_2)-1}{2}\right)$ , with values from zero to $\pi$ .

The passage around this formula

This expression follows from the Haar distribution of rotation angle, whose density on [0, $\pi$ ] is 2 $\sin^2(\theta/2)$ / $\pi$ . It passes the limiting checks: at $\epsilon$ =0 , blind success is zero; at $\epsilon$ = $\pi$ , it is one. The redundancy definition is informative only when 1- $\delta$ > $p_{\mathrm{blind}}(\epsilon)$ . Otherwise an empty box can qualify as a witness.

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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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See this notation across published equations →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.