Quantifying the imaginarity of quantum channels
摘要
Imaginary numbers are indispensable to the complete characterization of a quantum system’s dynamics. Recently, several imaginarity measures for quantum states and channels have been proposed from diverse perspectives. In this work, we quantify the imaginarity of quantum channels by leveraging their Choi representations and the quantum Jensen–Shannon divergence. Specifically, we put forward an imaginarity measure for quantum channels utilizing the quantum Jensen–Shannon divergence between the Choi state of a given quantum channel and that of its complex conjugate. We examine the fundamental properties of this measure and conduct a comparative analysis with two related existing imaginarity measures. To illustrate its utility, we explicitly calculate and analyze the imaginarity of a general unitary channel within the qubit system. Furthermore, a family of imaginarity measures can be analogously defined by adopting the generalized quantum Jensen–Shannon divergence. These measures provide a comprehensive family of new characterizations for the imaginarity of quantum channels.