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Equation 45 · Part 3 · The Entry a Relabeling Cannot Write

Symbol I

W†W=IW^\dagger W = I
II

What this part means

I is an input to the expression that computes the quantity on the left.

Its job in the formula

I is an input to the expression that computes the quantity on the left.

The passage around this formula

using only W†W^\dagger W = I . So DΛD_\Lambda = HfH_f - HfH_f = 0 , identically, as an operator, for every unitary W and every HfH_f . This is not a limit, an approximation, or a property of some special state; it is an algebraic identity that holds before any state is chosen at all.

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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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