Quantifying coherence of quantum channels based on the generalized \(\varvec{\alpha }\)-\(\varvec{z}\)-relative Rényi entropy

By using the Choi–Jamiołkowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized \(\alpha \) $\alpha$ -z-relative Rényi entropy. In addition, we present an alternative coherence measure of quantum channels by quantifying the commutativity between the channels and the completely dephasing channels with the generalized \(\alpha \) $\alpha$ -z-relative Rényi entropy. Some elegant properties of the measures are illustrated in detail. Explicit formulas of these coherence measures are derived for some detailed typical quantum channels.