Physical characterization of quantum devices from nonlocal correlations

TL;DR

This paper introduces SWAP, a theoretical tool combined with semi-definite methods, to better estimate physical properties of quantum devices from measurement data in a device-independent manner, surpassing previous techniques.

Contribution

The paper develops the SWAP method, enabling improved bounds and intractable case analysis for device-independent quantum property estimation using nonlocal correlations.

Findings

SWAP provides bounds orders of magnitude better than previous methods.

Enables robust self-testing of non-maximally entangled states.

Relates nonlocal correlations to work extraction and quantum dimensionality.

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.