### Abstract

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum χα2-divergence for some α∈ [ 0 , 1 ]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

Original language | English |
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Pages (from-to) | 2267-2290 |

Number of pages | 24 |

Journal | Letters in Mathematical Physics |

Volume | 107 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 1 2017 |

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### Keywords

- Positive definite operators
- Preservers
- Quantum χ -divergence

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*107*(12), 2267-2290. https://doi.org/10.1007/s11005-017-0989-0

**Maps on positive definite operators preserving the quantum χα2 -divergence.** / Chen, Hong Yi; Gehér, György Pál; Liu, Chih Neng; Molnár, L.; Virosztek, Dániel; Wong, Ngai Ching.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 107, no. 12, pp. 2267-2290. https://doi.org/10.1007/s11005-017-0989-0

}

TY - JOUR

T1 - Maps on positive definite operators preserving the quantum χα2 -divergence

AU - Chen, Hong Yi

AU - Gehér, György Pál

AU - Liu, Chih Neng

AU - Molnár, L.

AU - Virosztek, Dániel

AU - Wong, Ngai Ching

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum χα2-divergence for some α∈ [ 0 , 1 ]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

AB - We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum χα2-divergence for some α∈ [ 0 , 1 ]. We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.

KW - Positive definite operators

KW - Preservers

KW - Quantum χ -divergence

UR - http://www.scopus.com/inward/record.url?scp=85028988055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028988055&partnerID=8YFLogxK

U2 - 10.1007/s11005-017-0989-0

DO - 10.1007/s11005-017-0989-0

M3 - Article

VL - 107

SP - 2267

EP - 2290

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 12

ER -