# Quantum Coherence via Skew Information and Its Polygamy

## TL;DR

This paper introduces a new quantum coherence measure based on skew information, demonstrating its theoretical validity, operational meaning, and applications in coherence distribution, quantum correlations, and experimental measurement.

## Contribution

The paper proposes a novel coherence measure using skew information, proving its properties, operational relevance, and applications in coherence distribution and quantum correlations.

## Key findings

- The coherence measure satisfies all resource theory criteria.
- A polygamy relation for quantum coherence is established.
- Experimental measurement methods for the coherence measure are discussed.

## Abstract

Quantifying coherence is a key task in both quantum mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a certain broken observable. This coherence measure is proven to fulfill all the criteria (especially the strong monotonicity) recently introduced in the resource theories of quantum coherence. The coherence measure has an analytic expression and an obvious operational meaning related to quantum metrology. In terms of this coherence measure, the distribution of the quantum coherence, i.e., how the quantum coherence is distributed among the multiple parties is studied and a corresponding polygamy relation is proposed. As a further application, it is found that the coherence measure forms the natural upper bounds for quantum correlations prepared by incoherent operations. The experimental measurement of our coherence measure as well as the relative-entropy coherence, $l_p$-norm coherence is studied finally.