Operational view of the holographic information bound

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.

Figure 1

A measurement in the screen rest frame, with the $x$ direction orthogonal to the screen. The measurement takes place in the shaded space-time region set by the pixel size. Correspondingly, we will consider the acquired information to be located on the coarse-grained light sheet (depicted as a thick light ray), over an interval $\Delta \lambda$.