Inferring the Gibbs state of a small quantum system

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.

13 pages; v2: modified title, improved flow of exposition, additional appendices

References in corpus (5)

• Efficient quantum state tomography
• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• The Thermal Production of Strange and Non-Strange Hadrons in e+e- Collisions
• Quantum estimation via minimum Kullback entropy principle
• Evidence procedure for efficient quantum state tomography