Uncertainty of quantum channels based on symmetrized ρ-absolute variance and modified Wigner-Yanase skew information

Abstract We present the uncertainty relations in terms of the symmetrized ρ-absolute variance, which generalizes the uncertainty relations for arbitrary operators (not necessarily Hermitian) to quantum channels.By employing the quantity |Uρ|(Φ) proposed by Zhang et al. (2023 Quantum Inf. Process. 22, 456), we also establish tighter uncertainty relations for quantum channels by using the Cauchy-Schwarz inequality. Detailed examples are provided to illustrate the tightness of our results.