Equation 11 · Part 3 · The Entry a Relabeling Cannot Write
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
A coarse description reports less. It is built from a completely positive, trace-preserving map , a quantum channel sending fine states to coarse states, together with a coarse Hilbert space and a Hermitian coarse Hamiltonian on it. The simplest case is the partial trace over the bath, = [] with = ; nothing below depends on that particular choice, and a passive relabeling built from no discarding at all, treated next, is a channel too.
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
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Sources cited in the article section
These citations provide research context; check each source for the exact claim it supports.