# State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems

## TL;DR

This paper introduces a method for calculating tight, state-independent quantum uncertainty bounds applicable to noisy systems and POVMs, aiding entanglement detection where traditional criteria fail.

## Contribution

It provides a novel, guaranteed-error estimate method for optimal variance uncertainty relations, extending applicability to noisy environments and POVMs.

## Key findings

- Provides tight variance uncertainty bounds with error estimates
- Enables entanglement detection in noisy systems beyond traditional criteria
- Works for POVM measurements, broadening experimental applicability

## Abstract

Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal state-independent lower bound for the sum of the variances for any set of two or more measurements. The bounds come with a guaranteed error estimate, so results of pre-assigned accuracy can be obtained straightforwardly. Our method also works for POVM measurements. Therefore, it can be used for detecting entanglement in noisy environments, even in cases where conventional spin squeezing criteria fail because of detector noise.