Equation 41 · Part 6 · The Entry a Relabeling Cannot Write

subscript

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

subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

Full expressionsubscriptArticle meaning

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 subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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