### 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 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Chen, H. Y., Gehér, G. P., Liu, C. N., Molnár, L., Virosztek, D., & Wong, N. C. (2017). Maps on positive definite operators preserving the quantum χα2 -divergence.

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