Heisenberg Uncertainty Relation for Coarse-grained Observables

Abstract

We ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for coarse-grained measurements that are always valid, even for detectors with low precision. These relations should be particularly relevant in experimental demonstrations of squeezing in quantum optics, quantum state reconstruction, and the development of trustworthy entanglement criteria.

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• Heisenberg's Uncertainty Principle
• Continuous-variable quantum cryptography is secure against non-gaussian attacks
• Entropic Uncertainty Relations in Quantum Physics
• Entropic Entanglement Criteria for Continuous Variables
• Uncertainty inequalities as entanglement criteria for negative partial-transpose states
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Cited by in corpus (14)

• Imaging high-dimensional spatial entanglement with a camera
• Optimal Uncertainty Relations for Extremely Coarse-grained Measurements
• Reliable Entanglement Detection Under Coarse--Grained Measurements
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• Uncertainty Relations for coarse-grained measurements: an overview
• Gaussian states under coarse-grained continuous variable measurements
• Testing for entanglement with periodic coarse-graining
• General class of continuous variable entanglement criteria
• Detecting continuous variable entanglement in phase space with the $Q$-distribution
• Uncertainty relations for characteristic functions
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• On the lower bound of the Heisenberg uncertainty product in the Boltzmann states
• Transition to the classical regime in quantum mechanics on a lattice and implications of discontinuous space