Rong-Gen Cai, Li Hu, Shao-Jiang Wang

Recent progress on the black hole information paradox has reproduced the Page curve as required by the unitary evolution of the black hole entanglement entropy. In this Letter, we will argue that, the quantum speed limit on how fast a quantum system can evolve unitarily, when saturating the maximal information transmission bounds (Pendry's bound and Bremermann-Bekenstein bound), will slow down the would-be divergent rate of dynamical black hole entropy decreasing 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 Bremermann-Bekenstein bound on the de Sitter entanglement entropy exactly reproduces the trans-Planckian censorship conjecture, indicating that the would-be-ended inflating de Sitter space is the fastest receiver of information in nature.