# Entanglement propagation and typicality of measurements in the quantum Kac ring

## Abstract

We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurements in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22403396

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York)

- Additional Journal Information:
- Journal Volume: 348; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; HILBERT SPACE; MANY-BODY PROBLEM; MATHEMATICAL EVOLUTION; MEASURING METHODS; QUANTUM ENTANGLEMENT; QUANTUM SYSTEMS; RINGS; SPIN

### Citation Formats

```
Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de, Homrighausen, Ingo, and Kehrein, Stefan.
```*Entanglement propagation and typicality of measurements in the quantum Kac ring*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.05.019.

```
Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de, Homrighausen, Ingo, & Kehrein, Stefan.
```*Entanglement propagation and typicality of measurements in the quantum Kac ring*. United States. doi:10.1016/J.AOP.2014.05.019.

```
Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de, Homrighausen, Ingo, and Kehrein, Stefan. Mon .
"Entanglement propagation and typicality of measurements in the quantum Kac ring". United States. doi:10.1016/J.AOP.2014.05.019.
```

```
@article{osti_22403396,
```

title = {Entanglement propagation and typicality of measurements in the quantum Kac ring},

author = {Oberreuter, Johannes M., E-mail: johannes.oberreuter@theorie.physik.uni-goettingen.de and Homrighausen, Ingo and Kehrein, Stefan},

abstractNote = {We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurements in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.},

doi = {10.1016/J.AOP.2014.05.019},

journal = {Annals of Physics (New York)},

issn = {0003-4916},

number = ,

volume = 348,

place = {United States},

year = {2014},

month = {9}

}