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A local quantum operation on one tensor-factor subsystem acts as ${\Phi }_A\otimes {\mathrm{id}}_B$, with ${\Phi }_A$ completely positive. An individual outcome branch can decrease trace, while the sum over outcomes of a normalized instrument preserves trace. The unselected operation consequently leaves the remote reduced state unchanged. In a local field algebra, Kraus operators inside one region and commuting with a distant observable give an analogous no-signalling statement. Locality of the operation must be established; an arbitrary globally defined projection is not automatically a physically local measurement.