Heisenberg Uncertainty Relation for Coarse-grained Observables

TL;DR

This paper derives new, universally valid uncertainty relations for coarse-grained measurements in continuous variable quantum systems, addressing limitations of detector precision in experiments like quantum optics and entanglement detection.

Contribution

It introduces novel uncertainty relations tailored for low-precision measurements, enhancing the reliability of quantum state analysis and entanglement criteria.

Findings

Derived uncertainty relations valid for coarse-grained measurements

Applicable to low-precision detectors in quantum experiments

Facilitate more trustworthy quantum state reconstructions

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.