  Effects of nonmagnetic impurity doping in a spin ladder system with a spin
gap are investigated by the exact diagonalization as well as by the variational
Monte Carlo calculations. Substantial changes in macroscopic properties such as
enhancements in spin correlations and magnetic susceptibilities are observed in
the low impurity concentration region, which are caused by the increase of
low-energy states. These results suggest that small but finite amount of
nonmagnetic impurity doping relevantly causes the reduction or the vanishment
of the spin gap. This qualitatively explains the experimental result of
Zn-doped SrCu$_{2}$O$_{3}$ where small doping induces gapless nature. We
propose a possible scenario for this drastic change as a quantum phase
transition in a spin gapped ladder system due to spinon doping effects.
