Duality, monotonocity and the Wigner–Yanase–Dyson metrics
نویسنده
چکیده
We show that, for each value of α ∈ (−1, 1), the only Riemannian metrics on the space of positive definite matrices for which the ∇ and ∇ connections are mutually dual are matrix multiples of the Wigner-Yanase-Dyson metric. If we further impose that the metric be monotone, then this set is reduced to scalar multiples of the WignerYanase-Dyson metric.
منابع مشابه
Flat Connections and Wigner-yanase-dyson Metrics
On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the α-embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that in both cases, the existence of such a pair of connections is possible if and on...
متن کاملUncertainty Relation on Generalized Wigner-Yanase-Dyson Skew Information
We give a trace inequality related to the uncertainty relation of generalized Wigner-Yanase-Dyson skew information which is two parameter’s extension of our result in [12].
متن کاملJ ul 2 00 9 Uncertainty Relation on Wigner - Yanase - Dyson Skew Information
We give a trace inequality related to the uncertainty relation of Wigner-Yanase-Dyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S.Luo [6] for the quantum uncertainty quantity excluding the classical mixture.
متن کاملUncertainty Relation Based on Wigner-Yanase-Dyson Skew Information with Quantum Memory
We present uncertainty relations based on Wigner–Yanase–Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. It is shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed e...
متن کاملWigner-Yanase-Dyson Skew Information And Uncertainty Relation
We give a trace inequality related to the uncertainty relation of Wigner-YanaseDyson skew information. This inequality corresponds to a generalization of the uncertainty relation derived by S.Luo [8] for the quantum uncertainty quantity excluding the classical mixture. Finally we show a counter-example of the uncertainty relation related to WignerYanase-Dyson skew information given in [6] recen...
متن کامل