Inferring the Gibbs state of a small quantum system

TL;DR

This paper presents Bayesian methods for inferring Gibbs states of small quantum systems, addressing challenges like selecting relevant observables and accounting for prior biases in limited data scenarios.

Contribution

It introduces Bayesian model selection and interpolation techniques to improve Gibbs state inference in quantum systems with limited data.

Findings

Bayesian model selection effectively identifies relevant observables.

Bayesian interpolation reduces bias in parameter estimation.

Methods are demonstrated through simple quantum examples.

Abstract

Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the macroscopic realm, however, estimating a Gibbs state is a nontrivial inference task, due to two complicating factors: the proper set of relevant observables might not be evident a priori; and whenever data are gathered from a small sample only, the best estimate for the Lagrange parameters is invariably affected by the experimenter's prior bias. I show how the two issues can be tackled with the help of Bayesian model selection and Bayesian interpolation, respectively, and illustrate the use of these Bayesian techniques with a number of simple examples.