Physical characterization of quantum devices from nonlocal correlations

Abstract

In the device-independent approach to quantum information theory, quantum systems are regarded as black boxes which, 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 which, in combination with the tool of semi-definite 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 CHSH 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 non-maximally entangled two-qutrit states in the CGLMP 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.Comment: 17+2 pages, 10 figures, published versio

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“…McKague et al [127] give a more general framework for bipartite robust self-testing that subsumes the CHSH inequality, the Mayers-Yao self-test (simplifying [121]), as well as others. Yang and Navascués [170] give robust self-tests for any entangled two-qubit states, not just maximally entangled ones; the noise-resistance was further improved in [25]. McKague [125,126] and Miller and Shi [128] give results about self-testing of states shared by more than two parties.…”

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

“…On the other hand, the results of [9] and [50] do arrive at an ( )  O bound for self-testing. However, we know that their techniques cannot improve the asymptotic closeness, since we have shown in theorem 3 that this bound is optimal up to constant factors.…”

“…The result of [50] obtained numerically an even smaller factor of  2.2 by using a semidefinite programme. Their technique could, in principle, be used to improve our approach as well.…”

Robust self-testing of the three-qubitWstate

“…We present two approaches to robustness: the first one (subsection III A) is based on the analytic method first proposed in [6]; the second one (subsection III B) uses techniques based on semi-definite programming, following [11,16]. Both approaches are converted to fidelity for comparison.…”

“…The second method to study robustness follows the technique presented in [16] and, rather than using the 2-norm, uses the fidelity of the state (10) on the ancillary qubits with the W 3 state. This fidelity can be expressed in term of expectation values.…”