Entropic uncertainty relation based on generalized uncertainty principle

TL;DR

This paper investigates how the entropic uncertainty principle in quantum mechanics is modified by the generalized uncertainty principle inspired by quantum gravity, using Gaussian states and numerical methods, with implications for black hole physics.

Contribution

It introduces a modified entropic uncertainty relation incorporating the generalized uncertainty principle, linking quantum information theory with quantum gravity concepts.

Findings

Corrections to the entropic uncertainty relation are computed for small deformation parameters.

Numerical calculations support the theoretical modifications.

Potential implications for understanding black hole quantum properties.

Abstract

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.