Inferring the Gibbs state of a small quantum system

Details Inferring the Gibbs state of a small quantum system Inferring the Gibbs state of a small quantum system

2010-08-21

arxiv.org/abs/1008.3643v2

Phys. Rev. A 84, 012101 (2011)

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevA.84.012101

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.

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