# Decoherence for positive semigroups on M{sub 2}(C)

## Abstract

We extend Blanchard and Olkiewicz's definition of decoherence to open quantum systems whose dynamics are described by semigroups of positive (and not necessarily completely positive) operators on B(h). In particular, in the case h=C{sup 2}, we completely characterize the decomposition B(h)=M{sub 1}+M{sub 2} of B(h) in the sum of a decoherence-free part M{sub 1} and of a space M{sub 2} on which the semigroup vanishes with time.

- Authors:

- Dipartimento di Matematica, Universita di Pavia, via Ferrata 1, 27100 Pavia (Italy)
- Dipartimento di Matematica, Universita di Genova, Via Dodecaneso 35, 16146 Genova (Italy)

- Publication Date:

- OSTI Identifier:
- 21501285

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 52; Journal Issue: 3; Other Information: DOI: 10.1063/1.3560478; (c) 2011 American Institute of Physics; Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; GROUP THEORY; HILBERT SPACE; MATHEMATICAL MODELS; QUANTUM DECOHERENCE; QUANTUM MECHANICS; BANACH SPACE; MATHEMATICAL SPACE; MATHEMATICS; MECHANICS; SPACE

### Citation Formats

```
Carbone, Raffaella, Sasso, Emanuela, and Umanita, Veronica.
```*Decoherence for positive semigroups on M{sub 2}(C)*. United States: N. p., 2011.
Web. doi:10.1063/1.3560478.

```
Carbone, Raffaella, Sasso, Emanuela, & Umanita, Veronica.
```*Decoherence for positive semigroups on M{sub 2}(C)*. United States. doi:10.1063/1.3560478.

```
Carbone, Raffaella, Sasso, Emanuela, and Umanita, Veronica. Tue .
"Decoherence for positive semigroups on M{sub 2}(C)". United States. doi:10.1063/1.3560478.
```

```
@article{osti_21501285,
```

title = {Decoherence for positive semigroups on M{sub 2}(C)},

author = {Carbone, Raffaella and Sasso, Emanuela and Umanita, Veronica},

abstractNote = {We extend Blanchard and Olkiewicz's definition of decoherence to open quantum systems whose dynamics are described by semigroups of positive (and not necessarily completely positive) operators on B(h). In particular, in the case h=C{sup 2}, we completely characterize the decomposition B(h)=M{sub 1}+M{sub 2} of B(h) in the sum of a decoherence-free part M{sub 1} and of a space M{sub 2} on which the semigroup vanishes with time.},

doi = {10.1063/1.3560478},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 3,

volume = 52,

place = {United States},

year = {2011},

month = {3}

}

DOI: 10.1063/1.3560478

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