Manuscript I@2 · I.tex · lemma · 85631fa7
Lemma: Common sharp refinement
Context refinement and the Frauchiger–Renner example › Sharp contexts and transport · lines 2546–2561 · proof included or linked
I@2#lem:common-refinement
Two finite PVMs have a common sharp refinement if and only if every projector of one commutes with every projector of the other.
Proof. A common refinement expresses both families as sums of one orthogonal projector family, so the sums commute. Conversely, commuting projectors give the joint family
These are orthogonal projections summing to the identity and refine both PVMs.
Displayed formulas in this passage
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