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Equation 63 · Part 2 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol h

d(hg^,hg)=d(g^,g).d(h\hat g,hg)=d(\hat g,g).
hh

What this part means

h 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

h 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

The central mathematical test is simple to state. Apply a common frame transformation h to the physical description. Covariance sends g and g^\hat g to hg and hg^\hat g , or to the appropriate left/right action fixed by convention. A left-invariant distance satisfies d(hg^,hg)=d(g^,g)d(h\hat g,hg)=d(\hat g,g). The Haar measure is invariant, and the transformed POVM produces the correspondingly transformed outcome probabilities. Therefore the integration region defining success is merely relabeled. The value of pϵ(F)p_\epsilon(F) , and hence Rϵ,δR_{\epsilon,\delta} , should not change.

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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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Sources cited in the article section

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