Abstract
Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.
Highlights
One of the key traits of many-body quantum systems is that the full knowledge of their global configurations does not imply full knowledge of their constituents
We introduce a technical tool which is useful for establishing some fundamental relations between quantum covariance, quantum Fisher information and the metric adjusted skew information
A quantum Fisher information is extendable if its radial limit exists, and it is a Riemannian metric on the real projective space generated by the pure states
Summary
One of the key traits of many-body quantum systems is that the full knowledge of their global configurations does not imply full knowledge of their constituents. It has been proven that two-particle density matrices display quantum discord if, and only if, they are not “classical-quantum” states—that is, they are not (a mixture of) eigenvalues of local observables, ρ12 6= ∑i pi |i i1 hi | ⊗ ρ2,i , or ρ12 6= ∑i pi ρ1,i ⊗ |i i2 hi |, in which {|i i} is an orthonormal basis This is the only case in which one can identify a local measurement that does not change a bipartite quantum state, whose spectral decomposition reads A1 = ∑i λi |i i1 hi |, or A2 = ∑i λi |i i2 hi |. LQU was built as the minimum of the Wigner–Yanase skew information, a well-known information geometry measure [15], between a density matrix and a finite-dimensional observable (Hermitian operator) It quantifies how much a density matrix ρ12 is different from being a zero-discord state. LQU and IP are just two particular members of this family, allowing a unified treatment of their fundamental properties
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