We present ALMA Atacama Compact Array (ACA) 870 micron continuum maps of 28 infrared-bright SDSS quasars with Herschel/SPIRE detections at redshifts 2-4, the largest such sample ever observed with ALMA. The ACA detections are centred on the SDSS coordinates to within 1 arcsec for about 80 per cent of the sample. Larger offsets indicate that the far-infrared (FIR) emission detected by Herschel might come from a companion source. The majority of the objects (about 70 per cent) have unique ACA counterparts within the SPIRE beam down to 3-4 arcsec resolution. Only 30 per cent of the sample shows clear evidence for multiple sources with secondary counterparts contributing to the total 870 micron flux within the SPIRE beam to at least 25 per cent. We discuss the limitations of the data based on simulated pairs of point-like sources at the resolution of the ACA and present an extensive comparison of our findings with recent works on the multiplicities of sub-millimetre galaxies. We conclude that, despite the coarse resolution of the ACA, our data support the idea that, for a large fraction of FIR-bright quasars, the sub-mm emission comes from single sources. Our results suggest that, on average, optically bright quasars with strong FIR emission are not triggered by early-stage mergers but are, instead, together with their associated star formation rates, the outcome of either late-stage mergers or secular processes.
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