# 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.

- Authors:

- Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main (Germany)

- Publication Date:

- OSTI Identifier:
- 22038584

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; INTERPOLATION; LAGRANGE EQUATIONS; QUANTUM STATES; STATISTICAL MECHANICS; STATISTICAL MODELS

### Citation Formats

```
Rau, Jochen.
```*Inferring the Gibbs state of a small quantum system*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.012101.

```
Rau, Jochen.
```*Inferring the Gibbs state of a small quantum system*. United States. doi:10.1103/PHYSREVA.84.012101.

```
Rau, Jochen. Fri .
"Inferring the Gibbs state of a small quantum system". United States. doi:10.1103/PHYSREVA.84.012101.
```

```
@article{osti_22038584,
```

title = {Inferring the Gibbs state of a small quantum system},

author = {Rau, Jochen},

abstractNote = {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.},

doi = {10.1103/PHYSREVA.84.012101},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}