Quasi-Fine-Grained Uncertainty Relations

TL;DR

This paper introduces quasi-fine-grained uncertainty relations (QFGURs) that incorporate quantum memory, providing computable bounds linking uncertainty with entanglement and EPR steering, and unifying key quantum uncertainty frameworks.

Contribution

It generalizes fine-grained uncertainty relations to include quantum memory, offering a unified, computable framework connecting uncertainty, entanglement, and EPR steering.

Findings

QFGURs provide explicit bounds linking uncertainty with entanglement.

Framework unifies universal, memory-involved, and fine-grained uncertainty relations.

Reveals fundamental connections between uncertainty measures and quantum correlations.

Abstract

Nonlocality, which is the key feature of quantum theory, has been linked with the uncertainty principle by fine-grained uncertainty relations, by considering combinations of outcomes for different measurements. However, this approach assumes that information about the system to be fine-grained is local, and does not present an explicitly computable bound. Here, we generalize above approach to general quasi-fine-grained uncertainty relations (QFGURs) which applies in the presence of quantum memory and provides conspicuously computable bounds to quantitatively link the uncertainty to entanglement and Einstein-Podolsky-Rosen (EPR) steering, respectively. Moreover, our QFGURs provide a framework to unify three important forms of uncertainty relations, i.e., universal uncertainty relations, uncertainty principle in the presence of quantum memory, and fine-grained uncertainty relation. This result gives a direct significance to the uncertainty principle, and allows us to determine whether a quantum measurement exhibits typical quantum correlations, meanwhile, it reveals a fundamental connection between basic elements of quantum theory, specifically, uncertainty measures, combined outcomes for different measurements, quantum memory, entanglement and EPR steering.