# Markov property and strong additivity of von Neumann entropy for graded quantum systems

## Abstract

The quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. The additivity of von Neumann entropy for bipartite graded systems implies the statistical independence of states. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair of subsystems is nonseparable.

- Authors:

- Department of Mathematics, Graduate School of Science, Hokkaido University Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810 (Japan)

- Publication Date:

- OSTI Identifier:
- 20768746

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 47; Journal Issue: 3; Other Information: DOI: 10.1063/1.2176911; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ENTROPY; GAUGE INVARIANCE; MARKOV PROCESS; TENSORS; U-1 GROUPS; UNITARY SYMMETRY

### Citation Formats

```
Moriya, Hajime.
```*Markov property and strong additivity of von Neumann entropy for graded quantum systems*. United States: N. p., 2006.
Web. doi:10.1063/1.2176911.

```
Moriya, Hajime.
```*Markov property and strong additivity of von Neumann entropy for graded quantum systems*. United States. doi:10.1063/1.2176911.

```
Moriya, Hajime. Wed .
"Markov property and strong additivity of von Neumann entropy for graded quantum systems". United States. doi:10.1063/1.2176911.
```

```
@article{osti_20768746,
```

title = {Markov property and strong additivity of von Neumann entropy for graded quantum systems},

author = {Moriya, Hajime},

abstractNote = {The quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. The additivity of von Neumann entropy for bipartite graded systems implies the statistical independence of states. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair of subsystems is nonseparable.},

doi = {10.1063/1.2176911},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 3,

volume = 47,

place = {United States},

year = {2006},

month = {3}

}

DOI: 10.1063/1.2176911

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