Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses

TL;DR

This paper develops loss-tolerant linear steering inequalities for arbitrary dimensional states, demonstrating high robustness to noise and loss, and providing methods to certify non-joint measurability of measurements.

Contribution

It introduces a generic construction of loss-tolerant steering inequalities based on measurement overlaps, applicable to high-dimensional states, and links measurement efficiency to steering demonstration capabilities.

Findings

Critical detection efficiency for steering with n measurements is 1/n.

High-dimensional states enable robust steering demonstrations under loss.

The method certifies non-joint measurability of inefficient measurements.

Abstract

We show how to construct loss-tolerant linear steering inequalities using a generic set of von Neumann measurements that are violated by $d$-dimensional states, and that rely only upon a simple property of the set of measurements used (the maximal overlap between measurement directions). Using these inequalities we show that the critical detection efficiency above which $n$ von Neumann measurements can demonstrate steering is $1/n$. We show furthermore that using our construction and high dimensional states allows for steering demonstrations which are also highly robust to depolarising noise and produce unbounded violations in the presence of loss. Finally, our results provide an explicit means to certify the non-joint measurability of any set of inefficient von Neuman measurements.