Michał Banacki

We consider quantum statistics from the perspective of post-quantum no-signaling theories in which either none or only a certain number of systems are trusted. These scenarios can be fully described by so-called no-signaling boxes or no-signaling assemblages respectively. It has been shown so far that in the usual Bell non-locality scenario with a single measurement run, quantum correlations can never reproduce an extremal non-local point within the set of no-signaling boxes. We provide here a general no-go rule showing that the latter stays true even if arbitrary sequential measurements are allowed. On the other hand, we prove a positive result showing that already a single trusted qubit is enough for quantum theory to produce a self-testable extremal point within the corresponding set of no-signaling assemblages. This result provides a tool that opens up possibilities for security proofs of cryptographic protocols against general no-signaling adversaries in semi-device-independent scenarios.