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Equation 52 · A Reference Frame Becomes Classical by Publishing Its Orientation

What does this equation mean?

1−δ>pblind(ϵ)1-\delta>p_{\mathrm{blind}}(\epsilon)

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This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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δ\delta

Symbol delta

delta 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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pblindp_{\mathrm{blind}}

Symbol p_blind

pbp_blind 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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ϵ\epsilon

Symbol epsilon

epsilon 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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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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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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