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Equation 21 · The Entry a Relabeling Cannot Write

What does this equation mean?

DΛ:=Hf−Λ†(Hc).D_\Lambda := H_f - \Lambda^\dagger(H_c).

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Inputs and operationsH_f - Lambda^dagger(H_c)
Result or conditionD_Lambda :
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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DΛD_\Lambda

Symbol D_Lambda

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

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HfH_f

Symbol H_f

HfH_f is one of the signed contributions combined to compute the quantity on the left.

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Λ†\Lambda^\dagger

Symbol Lambda^dagger

the define.

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HcH_c

Symbol H_c

wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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subscript

subscript

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.

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How to interpret it

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What the article says around this equation

That pullback is the object this article is built around: DΛ:=Hf−Λ†(Hc)D_\Lambda := H_f - \Lambda^\dagger(H_c). DΛD_\Lambda is Hermitian on Hf\mathcal H_f — a positive, unital map applied to a self-adjoint input stays self-adjoint — and it carries units of energy, since both terms do. Its state-dependent reading,

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Sources cited in the article section

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