Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing

TL;DR

This paper presents a novel, device-independent framework using assemblage moment matrices to quantify quantum steerability, measurement incompatibility, and self-testing, enhancing quantum state and measurement characterization without assumptions.

Contribution

It introduces assemblage moment matrices for device-independent quantum characterization, linking steerability, entanglement robustness, and measurement incompatibility in a unified approach.

Findings

Lower bounds on quantum steerability from observed correlations.

Device-independent bounds on entanglement robustness and subchannel discrimination.

Explicit examples demonstrating self-testing of measurements.

Abstract

We introduce the concept of assemblage moment matrices, i.e., a collection of matrices of expectation values, each associated with a conditional quantum state obtained in a steering experiment. We demonstrate how it can be used for quantum states and measurements characterization in a device-independent manner, i.e., without invoking any assumption about the measurement or the preparation device. Specifically, we show how the method can be used to lower bound the steerability of an underlying quantum state directly from the observed correlation between measurement outcomes. Combining such device-independent quantifications with earlier results established by Piani and Watrous [Phys. Rev. Lett. 114, 060404 (2015)], our approach immediately provides a device-independent lower bound on the generalized robustness of entanglement, as well as the usefulness of the underlying quantum state for a type of subchannel discrimination problem. In addition, by proving a quantitative relationship between steering robustness and the recently introduced incompatibility robustness, our approach also allows for a device-independent quantification of the incompatibility between various measurements performed in a Bell-type experiment. Explicit examples where such bounds provide a kind of self-testing of the performed measurements are provided.