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Equation 63 · Part 1 · A Reference Frame Becomes Classical by Publishing Its Orientation

Symbol d

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

What this part means

d is part of the quantity the equation computes from the expression on the right.

Its job in the formula

d is part of the quantity the equation computes from the expression on the right.

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 function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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