Entanglement Detection Using Majorization Uncertainty Bounds

Abstract

Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement detection criteria based on quasi-entropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a comparator of disorder uniquely suited to information-theoretical applications are emphasized throughout.

10 pages, 1 figure

References in corpus (13)

• Quantum entanglement
• Entanglement detection
• Conditions for a class of entanglement transformations
• Optimization of entanglement witnesses
• Witnessing multipartite entanglement
• Entropic uncertainty relations - A survey
• Entanglement-assisted local manipulation of pure quantum states
• Separable states are more disordered globally than locally
• Entropic uncertainty relations and entanglement
• Separability conditions from entropic uncertainty relations
• Majorization Formulation of Uncertainty in Quantum Mechanics
• Note on Separability of the Werner states in arbitrary dimensions
• Correlative Capacity of Composite Quantum States

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• Improved tripartite uncertainty relation with quantum memory
• Majorization approach to entropic uncertainty relations for coarse-grained observables
• Strong entropic uncertainty relations for multiple measurements
• Optimal common resource in majorization-based resource theories
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Uncertainty under Quantum Measures and Quantum Memory
• Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
• Uniform Entanglement Frames
• Experimental investigation of majorization uncertainty relations in the high-dimensional systems
• Entanglement Detection via Direct-Sum Majorization Uncertainty Relations
• Witness High-Dimensional Quantum Steering via Majorization Lattice
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
• Spectral moments and entropy rigidity of quantum channels: a three-mode photonic witness