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Equation 43 · Part 3 · The Entry a Relabeling Cannot Write

Symbol W^dagger

Λ†(Oc)=W†OcW\Lambda^\dagger(O_c) = W^\dagger O_c W
W†W^\dagger

What this part means

WdW^dagger is an input to the expression that computes the quantity on the left.

Its job in the formula

WdW^dagger is an input to the expression that computes the quantity on the left.

The passage around this formula

The dual of conjugation by W is conjugation by W†W^\dagger : from the defining pairing, Tr\mathrm{Tr}[Wρ\rho W†W^\dagger OcO_c] = Tr\mathrm{Tr}[ρ\rho W†W^\dagger OcO_c W] holds for every ρ\rho , so Λ†(Oc)\Lambda^\dagger(O_c) = W†W^\dagger OcO_c W . Substituting,

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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