Uncertainty of quantum channels based on symmetrized \r{ho}-absolute variance and modified Wigner-Yanase skew information

Abstract

We present the uncertainty relations in terms of the symmetrized \r{ho}-absolute variance, which generalizes the uncertainty relations for arbitrary operator (not necessarily Hermitian) to quantum channels. By recalling the quantity |U\r{ho}|({\Phi}) proposed by Zhang et al. (Quantum Inf. Process. 22 456, 2023), which involves terms of more quantum mechanical nature. We also establish the tighter uncertainty relations for quantum channels by using Cauchy-Schwarz inequality. Detailed examples are provided to illustrate the tightness of our results.