Pointwise mutual information bounded by stochastic Fisher information

TL;DR

This paper establishes theoretical upper bounds linking pointwise mutual information with stochastic Fisher information, applicable to classical and quantum systems, and useful for quantum sensing and stochastic dynamics.

Contribution

It introduces general bounds connecting pointwise mutual information and stochastic Fisher information, extending to quantum systems and providing fundamental limits for information extraction.

Findings

Bounds hold in classical and quantum systems

Bounds deepen the connection between information theory and Fisher information

Results applicable to quantum sensing and stochastic dynamics

Abstract

We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These results deepen the connection between information-theoretical quantities and are shown to hold in general cases. We test the bounds in classical systems and provide a quantum generalization. Our results are useful for stochastic dynamics and quantum sensing, establishing fundamental theoretical limits for information extraction in single experimental realizations.