← Mathematical compendium

Published equation contexts

Tr[WρW†Oc]=Tr[ρW†OcW]\mathrm{Tr}[W\rho W^\dagger O_c] = \mathrm{Tr}[\rho W^\dagger O_c W]

Why this formula appears here

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

Read the full article-specific guide →

Read the representative guide

W†W^\dagger

Symbol W^dagger

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

Read this term in its guide →

How to interpret it

Read it with the definitions, units, and assumptions supplied by the article.

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

Tr[WρW†Oc]=Tr[ρW†OcW]\mathrm{Tr}[W\rho W^\dagger O_c] = \mathrm{Tr}[\rho W^\dagger O_c W]

Equation 41 · Evolutionary Physics

The Entry a Relabeling Cannot Write

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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

Meanings in this article

  • WW: the dual of conjugation by.
Equation guide → · Article →