Sample-Efficient Device-Independent Quantum State Verification and Certification

Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-\`{a}-vis verification devices the scenario with fully characterized measurement has been observed recent years. When it comes to uncharacterized measurements, so-called black-box scenario, practical methods are still rather scarce. Development self-testing an important step forward, but these results so far have used only by considering asymptotic behavior large, identically independently distributed (IID) samples resource. Such strong assumptions deprive procedure its truly device-independent character. In this paper, we develop systematic approach states free IID finite copy regime. Remarkably, show that can be performed optimal sample efficiency. Finally, case independent copies, protocol state certification: which fragment resource copies measured warrant rest close some target state.