  Uncertainty relation is a fundamental issue in quantum mechanics and quantum
information theory. By using modified generalized variance (MGV), and modified
generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total
and quantum uncertainty of quantum channels. The elegant properties of the
total uncertainty of quantum channels are explored in detail. In addition, we
present a trade-off relation between the total uncertainty of quantum channels
and the entanglement fidelity and establish the relationships between the total
uncertainty and entropy exchange/coherent information. Detailed examples are
given to the explicit formulas of the total uncertainty and the quantum
uncertainty of quantum channels. Moreover, utilizing a realizable experimental
measurement scheme by using the Mach-Zehnder interferometer proposed in Nirala
et al. (Phys Rev A 99:022111, 2019), we discuss how to measure the
total/quantum uncertainty of quantum channels for pure states.
