Black hole-de Sitter space as the fastest transmitter and receiver

TL;DR

This paper demonstrates that black holes and de Sitter space are the fastest information transmitters and receivers respectively, based on quantum speed limits and maximal information transmission bounds, with implications for cosmic censorship and trans-Planckian censorship.

Contribution

It reveals that black holes and de Sitter space saturate fundamental information bounds, establishing them as the fastest in their roles in nature.

Findings

Black holes are the fastest information transmitters.

De Sitter space acts as the fastest information receiver.

Quantum speed limits influence black hole entropy evolution.

Abstract

It is well-known that the unitary nature of black hole evaporation enforces its entropy evolution to follow the Page curve. In this Letter, we find that the quantum speed limit on how fast a quantum system can evolve unitarily, when the maximal information transmission bound is saturated, will slow down the would-be divergent decreasing rate of dynamical black-hole entropy at the very end of the Hawking evaporation, during which the Penrose inequality from cosmic censorship conjecture is exactly saturated. Therefore, an evaporating Schwarzschild black hole is the fastest transmitter of information in nature. Further applying the maximal information transmission bound to an effective-field-theory description of a de Sitter space would roughly reproduce the trans-Planckian censorship conjecture, indicating the de Sitter space as the fastest receiver of information in nature.