Average metric adjusted skew information of coherence under conical 2-designs generalized equiangular measurements

TL;DR

This paper introduces a new measure of quantum coherence based on metric adjusted skew information, analyzing its properties under conical 2-designs and deriving related trade-offs and entanglement criteria.

Contribution

It defines a novel coherence measure, proves its equivalence to scaled average coherence under various bases, and establishes new trade-off relations and entanglement criteria.

Findings

Proves the equivalence of the new measure to scaled average coherence.

Derives two trade-off relations involving the measure.

Provides two entanglement criteria validated by examples.

Abstract

Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under conical 2-designs generalized equiangular measurements, and prove the equivalence of this measure to the scaled average coherence based on metric adjusted skew information under a set of unitary groups, operator orthonormal bases, and mutually unbiased bases. We also derive two trade-off relations by this measure and solve a conjecture. Furthermore, we give two entanglement criteria by this measure and conical 2-designs generalized equiangular measurement, respectively, and illustrate the effectiveness of them by explicit examples.