Equation 47 · Part 1 · The Entry a Relabeling Cannot Write

Symbol W

W

W

What this part means

the dual of conjugation by.

Its job in the formula

W is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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

using only $W^\dagger$ W = I . So $D_\Lambda$ = $H_f$ - $H_f$ = 0 , identically, as an operator, for every unitary W and every $H_f$ . 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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See this notation across published equations →

The article lists its research sources here.