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

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Cited by in corpus (8)

• Entropy Distance: New Quantum Phenomena
• Pseudo-Bayesian Quantum Tomography with Rank-adaptation
• Non-canonical statistics of finite quantum system
• Assessing thermalization and estimating the Hamiltonian with output data only
• The initial system-bath state via the maximum-entropy principle
• Appearance of Gibbs states in quantum-state tomography
• Reconstructing the relaxation dynamics induced by an unknown heat bath
• Maximum Entropy competes with Maximum Likelihood