Variance-based uncertainty relations

TL;DR

This paper introduces state-independent variance-based uncertainty relations for multiple observables in finite-dimensional quantum systems, offering near-optimal bounds and applications in entanglement detection.

Contribution

It presents novel variance-based uncertainty relations that are state-independent and applicable to multiple observables, improving bounds and aiding entanglement detection.

Findings

Provides near-optimal lower bounds in typical examples

Enables entanglement detection using the new uncertainty relations

Extends uncertainty relations to multiple observables in finite dimensions

Abstract

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide near-optimal lower bounds in some typical examples, and are useful for entanglement detection.