Physical characterization of quantum devices from nonlocal correlations

In the device-independent approach to quantum information theory, quantum systems are regarded as black boxes that, given an input (the measurement setting), return an output (the measurement result). These boxes are then treated regardless of their actual internal working. In this paper we develop SWAP, a theoretical concept that, in combination with the tool of semidefinite methods for the characterization of quantum correlations, allows us to estimate physical properties of the black boxes from the observed measurement statistics. We find that the SWAP tool provides bounds orders of magnitude better than previously known techniques (e.g., for a Clauser-Horne-Shimony-Holt violation larger than 2.57, SWAP predicts a singlet fidelity greater than 70%). This method also allows us to deal with hitherto intractable cases such as robust device-independent self-testing of nonmaximally entangled two-qutrit states in the Collins-Gisin-Linden-Massar-Popescu scenario (for which Jordan's lemma does not apply) and the device-independent certification of entangled measurements. We further apply the SWAP method to relate nonlocal correlations to work extraction and quantum dimensionality, hence demonstrating that this tool can be used to study a wide variety of properties relying on the sole knowledge of accessible statistics.