# Quantum speed limits and the maximal rate of quantum learning

## TL;DR

This paper refines the fundamental limits on the rate of quantum information transfer by incorporating measurement back action and quantum speed limits, providing a more practical bound on quantum learning rates.

## Contribution

It extends the Bremermann-Bekenstein bound by explicitly including measurement back action and refined quantum speed limits, offering a more accurate upper bound on quantum learning rates.

## Key findings

- Derived a tractable expression using time-dependent perturbation theory
- Evaluated the bound for harmonic oscillator and Pöschl-Teller potential systems
- Showed the bound generalizes the classical Bremermann-Bekenstein limit

## Abstract

The Bremermann-Bekenstein bound is a fundamental bound on the maximal rate with which information can be transmitted. However, its derivation relies on rather weak estimates and plausibility arguments, which make the application of the bound impractical in the laboratory. In this paper, we revisit the bound and extend its scope by explicitly accounting for the back action of quantum measurements and refined expressions of the quantum speed limit. Our result can be interpreted as an upper bound on the maximal rate of quantum learning, and we show that the Bremermann-Bekenstein bound follows as a particular limit. Our results are illustrated, by first deriving a tractable expression from time-dependent perturbation theory, and then evaluating the bound for two time-dependent systems -- the harmonic oscillator and the P\"oschl-Teller potential.