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Equation 49 · A Reference Frame Becomes Classical by Publishing Its Orientation

What does this equation mean?

2sin⁡2(θ/2)/π2\sin^2(\theta/2)/\pi

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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θ\theta

Symbol θ

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

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π\pi

Symbol pi

the values from zero to.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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What the article says around this equation

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

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