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High-quality Ba_<1-x>K_xBiO_3 superconductors with a T_<ce> of 28.5 K were successfully synthesized using the plasma-arc melting and rapid-quenching (PMQ) method. X-ray powder diffraction data showed a single Ba_<0.6>K_<0.4>BiO_x structure with a lattice constant of a=4.283Å. The highest relative density was 97% of the theoretical density. Furthermore, the fabrication of an Au/MgO/Ba_<1-x>K_xBiO_3 tunnel-type junction was attempted on the PMQ-processed Ba_<1-x>K_xBiO_3 substrate. In I-V characteristics of Au/MgO/Ba_<1-x>K_xBiO_3 junctions, non-linearity was clearly observed at about 3 mV corresponding to the energy gap of Ba_<1-x>K_xBiO_3 superconductors. It was found that the PMQ-processed Ba_<1-x>K_xBiO_3 is more effective for some device applications than the powder samples produced by solid state reaction methods.