  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.
