← All parts of this equation

Equation 45 · Part 1 · The Entry a Relabeling Cannot Write

Symbol W^dagger

W†W=IW^\dagger W = I
W†W^\dagger

What this part means

WdW^dagger is part of the quantity the equation computes from the expression on the right.

Its job in the formula

WdW^dagger is part of the quantity the equation computes from the expression on the right.

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.

Read this part in the article →

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.

Open the illustrated exponents: repeated multiplication and powers guide →

See this notation across published equations →

The article lists its research sources here.