Inequalities for quantum skew information

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. Key words and phrases: Quantum covariance, metric adjusted skew information, Robertson-type uncertainty principle, operator monotone function, Wigner-Yanase-Dyson skew information.

References in corpus (5)

• Metric adjusted skew information
• Uncertainty Principle and Quantum Fisher Information - II
• The Wigner-Yanase entropy is not subadditive
• Uncertainty principle with quantum Fisher information
• Quantum covariance, quantum Fisher information and the uncertainty principle

Cited by in corpus (9)

• Geometric measures of quantum correlations: characterization, quantification, and comparison by distances and operations
• Schrödinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure
• Metric adjusted skew information: Convexity and restricted forms of superadditivity
• A unified approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information
• Convexity of quantum ${\chi }^2$-divergence
• Parity symmetry breaking of spin-$j$ coherent state superpositions in Gaussian noise channel
• Characterising two-sided quantum correlations beyond entanglement via metric-adjusted f-correlations
• Riemannian metrics on positive definite matrices related to means
• On a correspondence between regular and non-regular operator monotone functions