An operational view on the holographic information bound

TL;DR

This paper derives an operational interpretation of the covariant holographic entropy bound by linking quantum measurement uncertainties to geometric properties of light-sheets, suggesting a local limit on information based on area differences.

Contribution

It introduces an operational approach to the holographic entropy bound using quantum mechanics and geometry, providing a local version of the covariant entropy bound.

Findings

Derived an uncertainty relation connecting quantum measurement to geometric uncertainties.

Established a local operational version of the covariant entropy bound.

Linked the maximum decoded bits to the area difference of light-sheet surfaces.

Abstract

We study the covariant holographic entropy bound from an operational standpoint. Therefore we consider the physical limit for observations on a light-sheet. A light-sheet is a particular null hypersurface, and the natural measuring apparatus is a screen. By considering the physical properties of the screen - as dictated by quantum mechanics - we derive an uncertainty relation. This connects the number of bits of decoded information on the light-sheet to two geometric uncertainties: the uncertainty on the place where the bits are located and the uncertainty on the local expansion of the light-sheet. From this relation we can argue a local operational version of the (generalized) covariant entropy bound: the maximum number of bits decoded on a light-sheet interval goes like the area difference (in Planck units) of the initial and final surface spanned by the light rays.