Shannon Entropy Quantum Entanglement Criterion and the Generalized Uncertainty Principle

TL;DR

This paper investigates how quantum gravity effects, modeled by the generalized uncertainty principle, influence entropic uncertainty relations and the criteria for quantum entanglement, revealing increased bounds due to GUP corrections.

Contribution

It introduces GUP corrections to Shannon entropic uncertainty relations for entanglement, extending previous variance-based analyses and exploring fundamental quantum concepts.

Findings

GUP increases the upper bound for entanglement criteria.

GUP affects the entropic uncertainty relations in quantum systems.

The paper discusses fundamental links between GUP, entanglement, and uncertainty.

Abstract

We examine quantum gravity effects by applying the generalized uncertainty principle (GUP) to entropic uncertainty relation conditions on quantum entanglement. In particular, we study the GUP corrections to the Shannon entropic uncertainty condition for entanglement. As in an earlier paper [Blado, Herrera, Erwin arxiv:1706.10013 [quant-ph]] which dealt with variance relations, there is an increase in the upper bound for the entanglement condition upon the application of the generalized uncertainty principle. Fundamental concepts of the generalized uncertainty principle, entanglement and the entropic uncertainty relations are also discussed.