We present Atacama Large Millimeter/submillimeter Array (ALMA) 870um observations of 29 bright Herschel sources near high-redshift QSOs. The observations confirm that 20 of the Herschel sources are submillimeter-bright galaxies (SMGs) and identify 16 new SMG-QSO pairs that are useful to studies of the circumgalactic medium (CGM) of SMGs. Eight out of the 20 SMGs are blends of multiple 870um sources. The angular separations for six of the Herschel-QSO pairs are less than 10, comparable to the sizes of the Herschel beam and the ALMA primary beam. We find that four of these six pairs are actually QSOs hosted by SMGs. No additional submillimeter companions are detected around these QSOs and the rest-frame ultraviolet spectra of the QSOs show no evidence of significant reddening. Black hole accretion and star formation contribute almost equally in bolometric luminosity in these galaxies. The SMGs hosting QSOs show similar source sizes, dust surface densities, and SFR surface densities as other SMGs in the sample. We find that the black holes are growing $sim$3$times$ faster than the galaxies when compared to the present-day black-hole-galaxy mass ratio, suggesting a QSO duty cycle of $lesssim$30% in SMGs at z ~ 3. The remaining two Herschel-detected QSOs are undetected at 870um but each has an SMG companion only 9 and 12 away (71 and 95 kpc at z = 3). They could be either merging or projected pairs. If the former, they would represent a rare class of wet-dry mergers. If the latter, the QSOs would, for the first time, probe the CGM of SMGs at impact parameters below 100 kpc.
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