  Heisenberg's uncertainty relations for measurement quantify how well we can
jointly measure two complementary observables and have attracted much
experimental and theoretical attention recently. Here we provide an exact
tradeoff between the worst-case errors in measuring jointly two observables of
a qubit, i.e., all the allowed and forbidden pairs of errors, especially
asymmetric ones, are exactly pinpointed. For each pair of optimal errors we
provide an optimal joint measurement that is realizable without introducing any
ancilla and entanglement. Possible experimental implementations are discussed
and Toronto experiment [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] can
be readily adapted to an optimal joint measurement of two orthogonal
observables.
