## Abstract

We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations.

Original language | English |
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Pages (from-to) | 135-146 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 85 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 2008 Sep |

Externally published | Yes |

## Keywords

- Metric adjusted skew information
- Operator monotone function
- Quantum covariance
- Robertson-type uncertainty principle
- Wigner-Yanase-Dyson skew information.

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics