Quantum steering with imprecise measurements

TL;DR

This paper investigates how small measurement imprecisions affect quantum steering tests, revealing significant impacts on false positives and proposing an analytical method to account for imprecision in high-dimensional systems.

Contribution

It introduces a novel analytical approach to incorporate measurement imprecision into bipartite steering inequalities, improving the reliability of quantum steering tests.

Findings

Small measurement imprecision can cause false positives in steering tests.

The proposed bounds are analytical, easily computable, and optimal for certain steering scenarios.

The method applies to generalised quantum steering, not limited to separable states.

Abstract

We study quantum steering experiments without assuming that the trusted party can perfectly control their measurement device. Instead, we introduce a scenario in which these measurements are subject to small imprecision. We show that small measurement imprecision can have a large detrimental influence in terms of false positives for steering inequalities, and that this effect can become even more relevant for high-dimensional systems. We then introduce a method for taking generic measurement imprecision into account in tests of bipartite steering inequalities. The revised steering bounds returned by this method are analytical, easily computable, and are even optimal for well-known families of arbitrary-dimensional steering tests. Furthermore, it applies equally well to generalised quantum steering scenarios, where the shared quantum state does not need to be separable, but is instead limited by some other entanglement property.