Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality

TL;DR

This paper establishes a quantitative link between measurement incompatibility, quantum steering, and nonlocality, providing methods to estimate these phenomena and measurement incompatibility in a device-independent manner.

Contribution

It introduces a way to strengthen robustness-based quantifiers to provide lower bounds on measurement incompatibility, connecting these fundamental quantum properties quantitatively.

Findings

Robustness-based steering and nonlocality quantifiers can estimate measurement incompatibility.

Provides one-sided device-independent and device-independent bounds on measurement incompatibility.

Enhances understanding of the quantitative relationships between key quantum phenomena.

Abstract

The certification of Bell nonlocality or quantum steering implies the use of incompatible measurements. Here we make this connection quantitative. We show how to strengthen robustness-based steering and nonlocality quantifiers in order that they give strong lower bounds to previously proposed incompatibility quantifiers. Our results can be seen from two perspectives. On the one hand, they can be used to estimate how much steering or nonlocality can be demonstrated with a given set of measurements. On the other hand, they gives one-sided device-independent and device-independent ways of estimating measurement incompatibility.