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Equation 57 · Part 1 · The Entry a Relabeling Cannot Write

Symbol Lambda

Λ(ρ)=TrB[ρ]\Lambda(\rho) = \mathrm{Tr}_B[\rho]
Λ\Lambda

What this part means

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

Its job in the formula

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

The passage around this formula

Return to the genuine coarse-graining set aside earlier: Λ(ρ)\Lambda(\rho) = TrB\mathrm{Tr}_B[ρ\rho] , Hc\mathcal H_c = HS\mathcal H_S , HcH_c = HSH_S . The dual embeds a system observable back into the full space without touching the bath, Λ†(HS)\Lambda^\dagger(H_S) = HSH_S ⊗\otimes IBI_B , so

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Learn the underlying idea

A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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