Adjusting inequalities for detection-loophole-free steering experiments

TL;DR

This paper develops a method to modify steering inequalities for detection-loophole-free quantum steering experiments, ensuring reliable certification even with post-selection and varying detection efficiencies.

Contribution

It introduces a systematic way to find adjusted local-hidden-state bounds for steering inequalities in post-selected scenarios, applicable to multipartite systems and Bell nonlocality.

Findings

Modified steering inequalities certify steering above efficiency thresholds

Method extends to multipartite and Bell nonlocality scenarios

Examples demonstrate effectiveness of the approach

Abstract

We study the problem of certifying quantum steering in a detection-loophole-free manner in experimental situations that require post-selection. We present a method to find the modified local-hidden-state bound of steering inequalities in such a post-selected scenario. We then present a construction of linear steering inequalities in arbitrary finite dimension and show that they certify steering in a loophole-free manner as long as the detection efficiencies are above the known bound below which steering can never be demonstrated. We also show how our method extends to the scenarios of multipartite steering and Bell nonlocality, in the general case where there can be correlations between the losses of the different parties. In both cases we present examples to demonstrate the techniques developed.