Quantumness and Dequantumness Power of Quantum Channels

Focusing on the dynamics of quantumness in ensembles, we propose a framework to qualitatively and quantitatively characterize quantum channels from the perspective of the amount of quantumness in ensembles that a quantum channel can induce or reduce. Along this line, the quantumness power and dequantumness power are introduced. In particular, once a quantum dynamics described by time-varying quantum channels reduces the quantumness for any input ensembles all the time, we call it a completely dequantumness channel, whose relationship with Markovianity is analyzed through several examples.