Quantum speed limits and the maximal rate of information production

TL;DR

This paper derives quantum speed limit-based bounds on the maximum rate of information production in quantum systems, providing a more fundamental and less cosmologically dependent perspective on information processing limits.

Contribution

It introduces Bremermann-Bekenstein-type bounds derived solely from quantum information theory and quantum dynamics principles, avoiding cosmological assumptions.

Findings

Derived bounds for von Neumann entropy change rate in open systems

Established limits for Shannon information change in unitary evolution

Provided a more fundamental basis for quantum information processing limits

Abstract

The Bremermann-Bekenstein bound sets a fundamental upper limit on the rate with which information can be processed. However, the original treatment heavily relies on cosmological properties and plausibility arguments. In the present analysis, we derive equivalent statements by relying on only two fundamental results in quantum information theory and quantum dynamics -- Fannes inequality and the quantum speed limit. As main results, we obtain Bremermann-Bekenstein-type bounds for the rate of change of the von Neumann entropy in quantum systems undergoing open system dynamics, and for the rate of change of the Shannon information over some logical basis in unitary quantum evolution.