The central formula for a coarse-grained effective state is a direct restatement of a known quantum state pooling theorem, with no new proof or construction.
We will go through it su- perficially over the following lines, but for a deeper, detailed approach to the same topic we refer to [19]
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Effective state as compatibility between agents
The central formula for a coarse-grained effective state is a direct restatement of a known quantum state pooling theorem, with no new proof or construction.