### Abstract

In this article we consider certain kinds of metrics and relative entropies on sets of density operators acting on a finite-dimensional complex Hilbert space. The metrics are the ones induced by the von Neumann-Schatten p-norms. We describe the general form of 'a priori' nonsurjective isometries of the space of all density operators with respect to those distances. In the second part of this article we study mappings preserving entropic quantities. We determine the structure of 'a priori' nonsurjective maps on the set of all density operators which leave a certain measure of relative entropy invariant and also characterize the surjective maps on the set of all invertible density operators with similar invariance properties.

Original language | English |
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Pages (from-to) | 93-108 |

Number of pages | 16 |

Journal | Linear and Multilinear Algebra |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2012 |

### Fingerprint

### Keywords

- density operators
- isometries
- p-norms
- preservers
- relative entropies

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Linear and Multilinear Algebra*,

*60*(1), 93-108. https://doi.org/10.1080/03081087.2011.570267

**Isometries and relative entropy preserving maps on density operators.** / Molnár, L.; Nagy, Gergo.

Research output: Contribution to journal › Article

*Linear and Multilinear Algebra*, vol. 60, no. 1, pp. 93-108. https://doi.org/10.1080/03081087.2011.570267

}

TY - JOUR

T1 - Isometries and relative entropy preserving maps on density operators

AU - Molnár, L.

AU - Nagy, Gergo

PY - 2012/1

Y1 - 2012/1

N2 - In this article we consider certain kinds of metrics and relative entropies on sets of density operators acting on a finite-dimensional complex Hilbert space. The metrics are the ones induced by the von Neumann-Schatten p-norms. We describe the general form of 'a priori' nonsurjective isometries of the space of all density operators with respect to those distances. In the second part of this article we study mappings preserving entropic quantities. We determine the structure of 'a priori' nonsurjective maps on the set of all density operators which leave a certain measure of relative entropy invariant and also characterize the surjective maps on the set of all invertible density operators with similar invariance properties.

AB - In this article we consider certain kinds of metrics and relative entropies on sets of density operators acting on a finite-dimensional complex Hilbert space. The metrics are the ones induced by the von Neumann-Schatten p-norms. We describe the general form of 'a priori' nonsurjective isometries of the space of all density operators with respect to those distances. In the second part of this article we study mappings preserving entropic quantities. We determine the structure of 'a priori' nonsurjective maps on the set of all density operators which leave a certain measure of relative entropy invariant and also characterize the surjective maps on the set of all invertible density operators with similar invariance properties.

KW - density operators

KW - isometries

KW - p-norms

KW - preservers

KW - relative entropies

UR - http://www.scopus.com/inward/record.url?scp=84858591272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858591272&partnerID=8YFLogxK

U2 - 10.1080/03081087.2011.570267

DO - 10.1080/03081087.2011.570267

M3 - Article

AN - SCOPUS:84858591272

VL - 60

SP - 93

EP - 108

JO - Linear and Multilinear Algebra

JF - Linear and Multilinear Algebra

SN - 0308-1087

IS - 1

ER -