# Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir

## TL;DR

This paper studies how the entropic uncertainty relation in an atom-cavity system evolves under a structured bosonic reservoir, revealing dependencies on interactions, reservoir correlation time, and quantum memory, with methods to reduce uncertainty.

## Contribution

It provides a detailed analysis of entropic uncertainty dynamics in open quantum systems across Markovian and non-Markovian regimes, introducing a simple method to reduce uncertainty.

## Key findings

- Uncertainty depends on atom-cavity and cavity-reservoir interactions.
- Uncertainty is anti-correlated with the purity of the qubit state.
- Quantum weak measurement reversal can effectively reduce the uncertainty.

## Abstract

The uncertainty relation is a fundamental limit in quantum mechanics and is of great importance to quantum information processing as it relates to quantum precision measurement. Due to interactions with the surrounding environment, a quantum system will unavoidably suffer from decoherence. Here, we investigate the dynamic behaviors of the entropic uncertainty relation of an atom-cavity interacting system under a bosonic reservoir during the crossover between Markovian and non-Markovian regimes. Specifically, we explore the dynamic behavior of the entropic uncertainty relation for a pair of incompatible observables under the reservoir-induced atomic decay effect both with and without quantum memory. We find that the uncertainty dramatically depends on both the atom-cavity and the cavity-reservoir interactions, as well as the correlation time, $\tau$, of the structured reservoir. Furthermore, we verify that the uncertainty is anti-correlated with the purity of the state of the observed qubit-system. We also propose a remarkably simple and efficient way to reduce the uncertainty by utilizing quantum weak measurement reversal. Therefore our work offers a new insight into the uncertainty dynamics for multi-component measurements within an open system, and is thus important for quantum precision measurements.