Uncertainty of quantum channels via generalized Wigner–Yanase skew information

Abstract

Uncertainty relations are a distinctive characteristic of quantum physics. We provide a set of uncertainty relations for quantum channels based on the generalized Wigner–Yanase skew information. Both product-form and summation-form uncertainty inequalities are derived for two general quantum channels, which include the ones given by the Wigner–Yanase skew information as special cases. These uncertainty inequalities are further refined as uncertainty sequences. Detailed examples are given for several prototypical quantum channels.