  Millimeter emission from debris disks around stars of different ages provides
constraints on the collisional evolution of planetesimals. We present ALMA 1.3
millimeter observations of a sample of 76 Solar-type stars in the ~115 Myr old
Pleiades star cluster. These ALMA observations complement previous infrared
observations of this sample by providing sensitivity to emission from
circumstellar dust at lower temperatures, corresponding to debris at radii
comparable to the Kuiper Belt and beyond. The observations obtain a beam size
of 1.5 arcsec (200 au) and a median rms noise of 54 mircoJy/beam, which
corresponds to a fractional luminosity $L_{dust}/L_{star} \sim 10^{-4}$ for 40
K dust for a typical star in the sample. The ALMA images show no significant
detections of the targeted stars. We interpret these limits in the context of a
steady-state collisional cascade model for debris disk evolution that provides
a good description of observations of the field population near the Sun but is
not well-calibrated on younger populations.The ALMA non-detections of the
Pleiades systems are compatible with the disk flux predictions of this model.
We find no high fractional luminosity outliers from these ALMA data that could
be associated with enhanced collisions resulting from activity not accounted
for by steady-state evolution. However, we note that two systems (HII 1132 and
HD 22680) show 24 micron excess much higher than the predictions of this model,
perhaps due to unusually high dust production from dynamical events involving
planets.
