Joint measurement of two unsharp observables of a qubit

We present a single inequality as the necessary and sufficient condition for two unsharp observables of a two-level system to be jointly measurable in a single apparatus and construct explicitly the joint observables. A complementarity inequality arising from the condition of joint measurement, which generalizes Englert's duality inequality, is derived as the trade-off between the unsharpnesses of two jointly measurable observables.