Imprecise quantum steering inequalities in tripartite systems

TL;DR

This paper examines how measurement errors impact quantum steering inequalities, revealing that even small inaccuracies can significantly hinder the certification of steerability, especially in high-dimensional multipartite systems.

Contribution

It derives new bipartite and tripartite steering inequalities that account for measurement imperfections, highlighting their increased severity in multipartite quantum systems.

Findings

Small measurement errors can significantly impair steerability certification.

Measurement imperfections have a more severe impact in multipartite systems.

Theoretical framework provided for characterizing and mitigating measurement errors.

Abstract

Quantum steering, as a manifestation of nonlocal quantum correlations, plays a crucial role in enabling various quantum information processing tasks. However, practical implementations are often hindered by significant challenges arising from imperfect or untrusted measurement devices. This study investigates the impact of measurement inaccuracies on quantum steering, with a particular focus on errors in the untrusted party's measurement devices. We first analyze how such errors affect the evaluation of steering inequalities, and then derive bipartite steering inequalities based on correlation matrices under imperfect measurements. Our findings show that even small measurement errors can significantly compromise the certification of quantum steerability, an effect that becomes particularly pronounced as the system dimension increases. Furthermore, by extending the proposed steering inequality to a modified tripartite scenario via correlation matrices, we demonstrate that the influence of measurement imperfections is far more severe in multipartite quantum steering than in the bipartite case. Our results underscore the critical need to account for measurement imperfections in experimental quantum steering and provide a theoretical framework for characterizing and mitigating these effects in high-dimensional quantum systems.