Universal finite upper bound on entropy in quantum gravity

Prove the existence of a fundamental, universal finite upper bound on the von Neumann entropy accessible to an observer in consistent theories of quantum gravity, independent of system size or other parameters, under the measurement restrictions specified by the authors (measurements performed only in predetermined natural bases, with initial states taken as basis states or simple superpositions, and with at most a small number of measurements).

Background

Motivated by the finiteness of the Gibbons-Hawking entropy of de Sitter space (~10^122 for our universe), the paper proposes that quantum gravity may impose a universal finite upper bound on entropy accessible to any observer. The authors argue that unrestricted measurement schemes or contrived probability distributions can yield arbitrarily large entropy, and therefore impose reasonable restrictions on measurement bases, initial states, and the number of measurements to define physically relevant entropy generation processes.

Within this framework, they conjecture a size-independent upper bound, aiming to connect such a bound with cosmological observables and to test it via BMN string constructions. Establishing this bound would provide a conceptual foundation for estimating the cosmological constant from entropy considerations.