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A projection operator is one which when acts upon a quantum state (which is an element of a Hilbert space), "projects" it onto a subspace or onto another element of the same Hilbert space.
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Implications of commuting within the code space
The question:
I have a Hilbert space $\mathcal{H}=\mathcal{H}_A\otimes \mathcal{H}_B$, and a codespace $\mathcal{H}_{code}\subset \mathcal{H}$, so that $\mathcal{H}=\mathcal{H}_{code}\oplus\mathcal{ …