Definition: Matched equivalence

A matched operational equivalence consists of a bijection of experiment identifiers, a party relabelling in each experiment, and bijections of admitted instruments and outcomes preserving deterministic insertions and coarse-graining, with equality of matched complete probability tables.

It induces a raw-label bijection $f$. Such a self-equivalence is allowed when it preserves a datum, not merely when it maps between two distinct data presentations.