Self-testing is a procedure for characterizing quantum resources with the minimal level of trust. Up to now it has been used as a device-independent certification tool for particular quantum measurements, channels, and pure entangled states. In this work we introduce the concept of self-testing more general entanglement structures. More precisely, we present the first self-tests of an entangled subspace-the five-qubit code and the toric code. We show that all quantum states maximally violating a suitably chosen Bell inequality must belong to the corresponding code subspace, which remarkably includes also mixed states.
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Baccari et al. (2020) studied this question.
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