Entropic Uncertainty Relations with Quantum Memory in Accelerated Frames via Unruh-DeWitt Detectors

TL;DR

This paper explores how acceleration affects quantum uncertainty relations with quantum memory, revealing that Unruh effect can both increase or decrease uncertainty depending on initial quantum correlations.

Contribution

It analyzes the impact of acceleration on entropic uncertainty relations with quantum memory using Unruh-DeWitt detectors and reveals the nuanced role of quantum discord.

Findings

Acceleration does not always increase the uncertainty lower bound.

Initial quantum correlations influence whether uncertainty increases or decreases.

Higher quantum discord does not necessarily reduce measurement uncertainty.

Abstract

Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.