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.
- 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