Effects of Hawking radiation on the entropic uncertainty in a Schwarzschild space-time

TL;DR

This paper investigates how Hawking radiation influences the entropic uncertainty in a Schwarzschild space-time, revealing that higher Hawking temperatures increase measurement uncertainty and proposing strategies to mitigate this effect.

Contribution

It introduces a model analyzing entropic uncertainty near a black hole, linking Hawking radiation to measurement uncertainty, and suggests methods to reduce this uncertainty in relativistic quantum settings.

Findings

Higher Hawking temperatures inflate entropic uncertainty.

Measurement uncertainty correlates with the degree of mixing in particles.

A strategy to reduce uncertainty via non-tracing-preserved operations is proposed.

Abstract

Heisenberg uncertainty principle describes a basic restriction on observer's ability of precisely predicting the measurement for a pair of non-commuting observables, and virtually is at the core of quantum mechanics. We herein aim to study entropic uncertainty relation under the background of the Schwarzschild black hole and its control. Explicitly, we develop dynamical features of the measuring uncertainty via entropy in a practical model where a stationary particle interacts with its surrounding environment while another particle --- serving as a quantum memory reservoir --- undergoes freefall in the vicinity of the event horizon of the Schwarzschild space-time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, we provide a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a realistic scenario. Finally, an efficient strategy is proposed to reduce the uncertainty by non-tracing-preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space-time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.