# Decoherence of many-body systems due to many-body interactions

## Abstract

We study a spin-gas model, where N{sub S} system qubits are interacting with N{sub B} bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decoherence induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between bath qubits that are coupled to different individual system qubits and compare Markovian with non-Markovian scenarios. We derive a useful canonical form of a completely positive map that describes a class of system environment interactions with a finite size of environment correlations. As examples we consider specific quantum many-body states and investigate their evolution under different decoherence models. As a complementary investigation, we study how the coupling to the environment can be employed to generate a desired multipartite state.

- Authors:

- Institute for Theoretical Physics, University of Innsbruck, Innsbruck (Austria)
- (Austria)

- Publication Date:

- OSTI Identifier:
- 22038588

- 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; COUPLING; INTERACTIONS; MANY-BODY PROBLEM; MARKOV PROCESS; QUANTUM DECOHERENCE; QUBITS

### Citation Formats

```
Carle, T., Kraus, B., Briegel, H. J., and Institute for Quantum Optics and Quantum Information, Austrian Academy of Science, Innsbruck.
```*Decoherence of many-body systems due to many-body interactions*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.012105.

```
Carle, T., Kraus, B., Briegel, H. J., & Institute for Quantum Optics and Quantum Information, Austrian Academy of Science, Innsbruck.
```*Decoherence of many-body systems due to many-body interactions*. United States. doi:10.1103/PHYSREVA.84.012105.

```
Carle, T., Kraus, B., Briegel, H. J., and Institute for Quantum Optics and Quantum Information, Austrian Academy of Science, Innsbruck. Fri .
"Decoherence of many-body systems due to many-body interactions". United States. doi:10.1103/PHYSREVA.84.012105.
```

```
@article{osti_22038588,
```

title = {Decoherence of many-body systems due to many-body interactions},

author = {Carle, T. and Kraus, B. and Briegel, H. J. and Institute for Quantum Optics and Quantum Information, Austrian Academy of Science, Innsbruck},

abstractNote = {We study a spin-gas model, where N{sub S} system qubits are interacting with N{sub B} bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decoherence induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between bath qubits that are coupled to different individual system qubits and compare Markovian with non-Markovian scenarios. We derive a useful canonical form of a completely positive map that describes a class of system environment interactions with a finite size of environment correlations. As examples we consider specific quantum many-body states and investigate their evolution under different decoherence models. As a complementary investigation, we study how the coupling to the environment can be employed to generate a desired multipartite state.},

doi = {10.1103/PHYSREVA.84.012105},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}