Witness high-dimensional quantum steering via majorization lattice

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.