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Equation 41 · Part 4 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol hat g

MF(d(hg^))=UF(h)MF(dg^)UF(h)†.M_F(d(h\hat g))= U_F(h)M_F(d\hat g)U_F(h)^\dagger.
g^\hat g

What this part means

hat g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

hat g is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

The passage around this formula

An estimator is generated by a positive-operator-valued measure MF(dg^)M_F(d\hat g) on the fragment. Covariance requires that rotating the encoded state by h rotates the distribution of estimates by the same group action. In schematic form, MF(d(hg^))=UF(h)MF(dg^)UF(h)†M_F(d(h\hat g))= U_F(h)M_F(d\hat g)U_F(h)^\dagger. Group-covariant estimation is established machinery. Bagan, Baig, and Muñoz-Tapia derived optimal strategies for transmitting and estimating Cartesian frames with finite spin systems [ 5 ] . Chiribella, D’Ariano, and Sacchi treated optimal estimation of group transformations under a class of invariant cost functions and connected the construction directly to reference-frame transmission [ 6 ] . The novelty proposed here is not the covariant…

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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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Sources cited in the surrounding passage

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