Generalized entropic uncertainty relation and non-classicality in Schwarzschild black hole

TL;DR

This paper introduces a new, tighter entropic uncertainty relation applicable to many-body systems, demonstrating its relevance in Schwarzschild black holes and revealing insights into quantum coherence, entanglement, and non-classicality in curved spacetime.

Contribution

It proposes a generalized entropic uncertainty relation with a tighter bound and explores its implications in black hole physics, linking quantum coherence and entanglement.

Findings

Derived a tighter entropic uncertainty bound for multi-measurement systems.

Established the exact equivalence between entanglement and $l_1$-norm coherence for GHZ states.

Showed that quantum coherence decreases and uncertainty increases with Hawking temperature.

Abstract

The uncertainty principle constitutes a fundamental pillar of quantum theory, representing one of the most distinctive features that differentiates quantum mechanics from classical physics. In this study, we firstly propose a novel generalized entropic uncertainty relation (EUR) for arbitrary multi-measurement in the many-body systems, and rigorously derive a significantly tighter bound compared to existing formulations. Specifically, we discuss the proposed EUR in the context of Schwarzschild black hole, where we demonstrate the superior tightness of our derived bound. The study further elucidates the dynamical evolution of multipartite quantum coherence and entanglement in the curved spacetime. A particularly noteworthy finding reveals the exact equivalence between entanglement and $l_1$-norm coherence for arbitrary $N$-partite Greenberger-Horne-Zeilinger-type (GHZ-type) states. Moreover, we find that quantum coherence is significantly diminished and the measurement uncertainty increases to a stable maximum with increasing Hawking temperature. Thus, the findings of this study contribute to a deeper understanding of non-classicality and quantum resources in black holes.