We investigate distinguishability (measured by fidelity) of the initial and the final state of a qubit, which is an object of the so-called nonideal quantum measurement of the first kind. We show that the fidelity of a nonideal measurement can be greater than the fidelity of the corresponding ideal measurement. This result is somewhat counterintuitive, and can be traced back to the quantum parallelism in quantum operations, in analogy with the quantum parallelism manifested in the quantum computing theory. In particular, while the quantum parallelism in quantum computing underlies efficient quantum algorithms, the quantum parallelism in quantum information theory underlies this, classically unexpected, increase of the fidelity.

13 pages, 1 color figure, uses tole2.sty, psfig.tex