Maximal quantum CHSH inequality violation certifies an embedded maximally entangled qubit pair and its ideal measurement action, up to local isometries and unused ancillary systems, under the separated-device quantum assumptions. It does not identify every microscopic component of an arbitrary device. Near-maximal observed correlations require robust error bounds rather than exact identification.[ref]
Robust Self Testing of the Singlet by Matthew McKague and others. Robust Self Testing of the Singlet, arXiv:1203.2976, abstract: local bases isolate an approximate EPR pair, potentially encoded within a larger environment or ancilla
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