Witness High-Dimensional Quantum Steering via Majorization Lattice
arXiv:2507.20950 · doi:10.1038/s41534-026-01204-3
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.
43 pages, 4 figures, 3 tables
References in corpus (42)
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Conditions for a class of entanglement transformations
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Quantum Steering
- Entanglement, EPR-correlations, Bell-nonlocality, and Steering
- High-dimensional quantum communication: benefits, progress, and future challenges
- Quantum steering: a review with focus on semidefinite programming
- Experimental EPR-Steering of Bell-local States
- Experimental Quantum Cryptography with Qutrits
- Provably-Secure and High-Rate Quantum Key Distribution with Time-Bin Qudits
- EPR Steering Inequalities from Entropic Uncertainty Relations
- Separable states are more disordered globally than locally
- Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
- Beating the channel capacity limit for superdense coding with entangled ququarts
- Entropic uncertainty relations and entanglement
- One-to-one mapping between steering and joint measurability problems
- Universal Uncertainty Relations
- Majorization entropic uncertainty relations
- Strong Majorization Entropic Uncertainty Relations
- Genuine High-Order Einstein-Podolsky-Rosen Steering
- Noise robustness of the nonlocality of entangled quantum states
- Maximal randomness expansion from steering inequality violations using qudits
- Genuine high-dimensional quantum steering
- Quantifying measurement incompatibility of mutually unbiased bases
- Steering criteria from general entropic uncertainty relations
- Incompatibility robustness of quantum measurements: a unified framework
- Majorization Formulation of Uncertainty in Quantum Mechanics
- Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
- Tight steering inequalities from generalized entropic uncertainty relations
- Most incompatible measurements for robust steering tests
- Loss-tolerant EPR steering for arbitrary dimensional states: joint measurability and unbounded violations under losses
- Retrieving High-Dimensional Quantum Steering From a Noisy Environment with N Measurement Settings
- Multipartite steering inequalities based on entropic uncertainty relations
- The Optimal Uncertainty Relation
- Entanglement Detection Using Majorization Uncertainty Bounds
- Majorization uncertainty relations for mixed quantum states
- Tighter Einstein-Podolsky-Rosen steering inequality based on the sum uncertainty relation
- Exact Steering Bound for Two-Qubit Werner States
- Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
- Complete hierarchy for high-dimensional steering certification
- Compatibility of Generalized Noisy Qubit Measurements
- Semidefinite relaxations for high-dimensional entanglement in the steering scenario