An Uncertainty Relation for Measurements of Random Unitary Channels Acting on a Qubit

Abstract

By preparing an input state and measuring an observable for the output state, we can measure a quantum channel. Following the formulation given by Xiao et al., we study an uncertainty relation for ancilla-free measurements of random unitary channels acting on a qubit. We obtain an explicit formula and give a necessary and sufficient condition for this formula to be nontrivial.