  The conceptual relation between the measurability of quantum mechanical
observables and the computability of numerical functions is re-examined. A new
formulation is given for the notion of measurability with finite precision in
order to reconcile the conflict alleged by M. A. Nielsen [Phys. Rev. Lett. 79,
2915 (1997)] that the measurability of a certain observable contradicts the
Church-Turing thesis. It is argued that any function computable by a quantum
algorithm is a recursive function obeying the Church-Turing thesis, whereas any
observable can be measured in principle.
