Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole

TL;DR

This paper investigates how Hawking radiation in Garfinkle-Horowitz-Strominger black holes affects the entropic uncertainty relation, quantum correlations, and secret key rate, revealing the influence of curved spacetime on quantum information.

Contribution

It introduces a model analyzing entropic uncertainty in GHS black holes considering Hawking radiation's impact on quantum correlations and cryptographic security.

Findings

Hawking radiation increases the entropic uncertainty lower bound.

Quantum correlations decrease due to Hawking radiation near the black hole.

Hawking radiation impacts the quantum secret key rate.

Abstract

Heisenberg's uncertainty principle is a fundamental element in quantum mechanics. It sets a bound on our ability to predict the measurement outcomes of two incompatible observables simultaneously. In quantum information theory, the uncertainty principle can be expressed using entropic measures. The entropic uncertainty relation can be improved by considering an additional particle as a memory particle. The presence of quantum correlation between the memory particle and the measured particle reduces the uncertainty. In a curved space-time, the presence of the Hawking radiation can reduce quantum correlation. Therefore, concerning the relationship between the quantum correlation and entropic uncertainty lower bound, we expect that the Hawking radiation increases the entropic uncertainty lower bound. In this work, we investigate the entropic uncertainty relation in Garfinkle-Horowitz-Strominger (GHS) dilation black hole. We consider a model in which the memory particle is located near the event horizon outside the black hole, while the measured particle is free falling. To study the proposed model, we will consider examples with Dirac fields. We also explore the effect of the Hawking radiation on the quantum secret key rate.