# Average coherence with respect to complementary measurements

## TL;DR

This paper studies the average quantum coherence relative to complete sets of measurements using a specific coherence measure, deriving relations among different measurement types.

## Contribution

It introduces an analytical framework for evaluating and relating average coherence across mutually unbiased and symmetric informationally complete measurements.

## Key findings

- Derived analytical relations among average coherences for different measurement sets.
- Evaluated average coherence using Wigner-Yanase skew information-based measure.
- Provided insights into the structure of quantum coherence in measurement contexts.

## Abstract

We investigate the average coherence with respect to a complete set of complementary measurements. By using a Wigner-Yanase skew information-based coherence measure introduced in [Phys. Rev. A \textbf{96}, 022130, 2017], we evaluate the average coherence of a state with respect to any complete set of mutually unbiased measurements and general symmetric informationally complete measurements, respectively. We also establish analytically the relations among these average coherences.