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.

arXiv comment6 pages, final version

References in corpus (33)

• The Uncertainty Principle in the Presence of Quantum Memory
• Heisenberg's Uncertainty Principle
• Entropic uncertainty relations - A survey
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Proof of Heisenberg's error-disturbance relation
• Improved entropic uncertainty relations and information exclusion relations
• Entropic uncertainty relations and entanglement
• Universal Uncertainty Relations
• Majorization entropic uncertainty relations
• Strong Majorization Entropic Uncertainty Relations
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Entropic Uncertainty Relations in Quantum Physics
• Entropic Entanglement Criteria for Continuous Variables
• Violation of Continuous Variable EPR Steering with Discrete Measurements
• Majorization Formulation of Uncertainty in Quantum Mechanics
• Fine-grained lower limit of entropic uncertainty in the presence of quantum memory
• Quantum and classical entropic uncertainty relations
• Improved bounds in entropic uncertainty relations
• General entropy-like uncertainty relations in finite dimensions
• On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles
• A min-entropy uncertainty relation for finite size cryptography
• Entropic uncertainty from effective anti-commutators
• Reliable Entanglement Detection Under Coarse--Grained Measurements
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• State-Dependent Approach to Entropic Measurement-Disturbance Relations
• Entanglement Detection Using Majorization Uncertainty Bounds
• On a generalized entropic uncertainty relation in the case of the qubit
• Comment on "Improved bounds on entropic uncertainty relations"
• Shannon entropy as a measure of uncertainty in positions and momenta
• Improving Einstein-Podolsky-Rosen Steering Inequalities with State Information
• Missing data outside the detector range: application to continuous variable entanglement verification and quantum cryptography
• Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures
• Uncertainty related to position and momentum localization of a quantum state

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• Variance-based uncertainty relations for incompatible observables
• Multi-observable Uncertainty Relations in Product Form of Variances
• Continuous-Variable Protocol for Oblivious Transfer in the Noisy-Storage Model
• The Conditional Uncertainty Principle
• Uncertainty, joint uncertainty, and the quantum uncertainty principle
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Majorization entropic uncertainty relations for quantum operations
• Majorization uncertainty relations for mixed quantum states
• Certainty relations, mutual entanglement and non-displacable manifolds
• Uncertainty Relations for coarse-grained measurements: an overview
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Entropic measures of joint uncertainty: effects of lack of majorization
• Quantum Uncertainty Principles for Measurements with Interventions
• On entropic uncertainty relations in the presence of a minimal length
• Continuous majorization in quantum phase space
• Uncertainty-Reality Complementarity and Entropic Uncertainty Relations
• Uncertainty relations for characteristic functions
• Tripartite measurement uncertainty in Schwarzschild space-time
• Conditional entropic uncertainty relations for Tsallis entropies
• Sum uncertainty relations based on $(\alpha ,\beta ,\gamma )$ weighted Wigner-Yanase-Dyson skew information
• Control of particle propagation beyond the uncertainty limit by interference between position and momentum
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• 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 successive measurements in the presence of a minimal length
• Tighter uncertainty relations based on $(\alpha ,\beta ,\gamma )$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information
• Rényi and Tsallis formulations of separability conditions in finite dimensions
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