A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

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.

Complementary measurement-induced quantum uncertainty based on metric adjusted skew information

We investigate complementary measurement-induced quantum uncertainty based on metric adjusted skew information, and propose two new measures of quantum uncertainty associated with mutually unbiased measurements and general symmetric informationally complete measurements, respectively. Based on these measures of quantum uncertainty, we present two entanglement criteria and show that they detect better entanglement than the existing corresponding criteria by detailed examples.

Quantum uncertainty based on metric adjusted skew information

Prompted by the open questions in Gibilisco [P. Gibilisco, Fisher information and means: Some questions in the classical and quantum settings, Int. J. Software Informatics 8 (2014) 265–276], he introduced a family of measurement-induced quantum uncertainty measures via metric adjusted skew informations, we investigate these measures’ fundamental properties (including basis independence and spectral representation), and illustrate their applications to detect quantum nonlocality and entanglement.