Majorization approach to entropic uncertainty relations for coarse-grained observables

Abstract

We improve the entropic uncertainty relations for position and momentum coarse-grained measurements. We derive the continuous, coarse-grained counterparts of the discrete uncertainty relations based on the concept of majorization. The obtained entropic inequalities involve two Rényi entropies of the same order, and thus go beyond the standard scenario with conjugated parameters. In a special case describing the sum of two Shannon entropies the majorization-based bounds significantly outperform the currently known results in the regime of larger coarse graining, and might thus be useful for entanglement detection in continuous variables.

6 pages, final version

References in corpus (7)

• Heisenberg's Uncertainty Principle
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
• Improved bounds in entropic uncertainty relations
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Entanglement Detection Using Majorization Uncertainty Bounds
• Uncertainty related to position and momentum localization of a quantum state

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• Uncertainty relations based on Wigner-Yanase skew information
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Summation and product forms of uncertainty relations based on metric-adjusted skew information
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole
• Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information