Witness High-Dimensional Quantum Steering via Majorization Lattice

TL;DR

This paper introduces a majorization lattice framework for detecting quantum steering across arbitrary dimensions and measurement settings, surpassing previous methods in stringency and scope.

Contribution

The authors develop a novel majorization lattice approach for quantum steering detection applicable to high-dimensional systems and diverse measurement scenarios, improving detection capabilities.

Findings

Derived steering inequalities for various quantum states

Achieved more stringent detection bounds than previous results

Revealed that existing high-dimensional results are approximate limits

Abstract

Quantum steering enables one party to influence another remote quantum state by local measurement. While steering is fundamental to many quantum information tasks, the existing detection methods in the literature are mainly constrained to either specific measurement scenario or low-dimensional systems. In this work, we propose a majorization lattice framework for steering detection, which is capable of exploring the steering in arbitrary dimension and measurement setting. Steering inequalities for two-qubit states, high-dimensional Werner states and isotropic states are obtained, which set even stringent bars than what has been reached yet. Notably, the known high-dimensional results turn out to be some kind of approximate limits of the new approach.