Measurement-device-independent measure of steerability and witnesses for all steerable resources

TL;DR

This paper introduces a measurement-device-independent method to detect and quantify steerability in quantum resources, using witnesses and a new steerability measure, without assumptions on the state or measurements.

Contribution

It systematically constructs MDI witnesses for all steerable assemblages and defines the first MDI steerability measure, proving its equivalence to steering robustness.

Findings

All steerable assemblages can be detected with the proposed witnesses.

The introduced measure is a valid steering monotone.

The method does not require characterization of detectors or the underlying state.

Abstract

The fact that nonlocality implies steering enables one to certify steerability by using a Bell inequality violation. Such a certification is device-independent (DI), i.e., one makes no assumption neither on the underlying state nor on the measurements. However, not all steerable states can violate a Bell inequality. Here, we systematically construct a collection of witnesses for steerable resources, defined by assemblages, in a measurement-device-independent (MDI) scenario. The inputs driving the measurement are replaced by a set of tomographically complete quantum states, and neither the detectors nor the underlying state is characterized. We show that all steerable assemblages can be detected by properly chosen witnesses. Furthermore, we introduce the first measure of steerability in an MDI scenario and show that such a measure is a standard one, i.e., a steering monotone, by proving that it is equivalent to the steering robustness.