Quantifying coherence relative to channels via metric-adjusted skew information

In terms of the metric-adjusted skew information (an important and versatile class of quantum Fisher information), which generalizes the seminal Wigner-Yanase skew information arising naturally from the study of quantum measurement, we propose a family of coherence measures of states relative to quantum channels, and reveal their basic properties such as unitary covariance, convexity, and monotonicity. Furthermore, we evaluate these coherence measures of states relative to several prototypical quantum channels, and make a comparative study for this family of coherence measures with relative entropy of coherence. This provides a general approach to coherence of states relative to quantum channels, which also captures decoherence on the states caused by quantum channels and asymmetry of states relative to quantum channels.

Automated summary

The paper proposes a family of coherence measures for states relative to quantum channels based on metric-adjusted skew information. The basic properties of these measures, such as unitary covariance, convexity, and monotonicity, are revealed. The coherence measures are evaluated for various prototypical quantum channels and compared with relative entropy of coherence. This provides a general approach to studying coherence of states relative to quantum channels, capturing decoherence and asymmetry caused by quantum channels.