Equation 41 · Part 1 · The Entry a Relabeling Cannot Write

Symbol W

\mathrm{Tr}[W\rho W^\dagger O_c] = \mathrm{Tr}[\rho W^\dagger O_c W]

W

What this part means

the dual of conjugation by.

Its job in the formula

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

Full expressionSymbol WArticle meaning

Where the article explains it

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

The passage around this formula

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

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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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