Stability of Maximum-Entropy Inference in Finite Dimensions

TL;DR

This paper rigorously analyzes the stability and convergence properties of maximum-entropy inference in finite-dimensional quantum systems, providing explicit bounds and demonstrating robustness under certain quantum operations.

Contribution

It establishes quantitative stability results for maximum-entropy inference, linking data deviations to state convergence, and shows these results are stable under unital completely positive maps.

Findings

Convergence of moments and entropy implies convergence of quantum states in trace norm.

Explicit bounds relate data and entropy deviations to state distance.

Results are stable under unital completely positive maps.

Abstract

We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The maximum-entropy principle selects the Gibbs state that agrees with the data while remaining maximally unbiased. We prove that convergence of moments and entropy implies convergence of states in trace norm, derive explicit quantitative bounds linking data and entropy deviations to state distance, and show that these results are stable under unital completely positive maps. The analysis is self-contained and relies on convex duality, relative entropy, and Pinsker-type inequalities, providing a rigorous and unified foundation for finite-dimensional maximum-entropy inference.