Characterizing Nonlocal Correlations via Universal Uncertainty Relations

Abstract

Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. In the course of our study, the uncertainty relations are formulated in majorization form, and the uncertainty quantifier can be chosen as any convex Schur concave functions, this leads to a large set of inequalities, including all existing criteria based on entropies. We address the question that if all steerable states (or entangled states) can be witnessed by some uncertainty-based inequality, we find that for pure states and many important families of states, this is the case.

References in corpus (10)

• Entanglement detection
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Observation of one-way Einstein-Podolsky-Rosen steering
• The uncertainty principle determines the non-locality of quantum mechanics
• Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks
• Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurement
• Fine-grained EPR-steering inequalities
• All entangled pure states violate a single Bell's inequality

Cited by in corpus (13)

• Quantum Steering
• Tight $N$-observable uncertainty relations and their experimental demonstrations
• Experimental investigation of multi-observable uncertainty relations
• Entanglement detection by violations of noisy uncertainty relations: A proof of principle
• Incompatibility of Observables as State-Independent Bound of Uncertainty Relations
• Quasi-Fine-Grained Uncertainty Relations
• Averaged fidelity-based steering criteria
• Diagnosing steerability of a bipartite state with the nonsteering threshold
• Tight bounds from multiple-observable entropic uncertainty relations
• Quantum work fluctuations versus macrorealism in terms of non-extensive entropies
• Multiparticle Entanglement Resolution Analyzer based on Quantum-Control-Assisted Uncertainty Relation
• Experimental investigation of majorization uncertainty relations in the high-dimensional systems
• The Diminished Quantum Uncertainty in Multipartite Entanglement