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We present ALMA CO(2-1) spectroscopy of 6 massive (log$_{10}$M$_{\rm{*}}/\rm{M}_\odot>$11.3) quiescent galaxies at $z\sim1.5$. These data represent the largest sample using CO emission to trace molecular gas in quiescent galaxies above $z>1$, achieving an average 3$σ$ sensitivity of M$_{\rm{H_{2}}}\sim10^{10}\rm{M}_\odot$. We detect one galaxy at 4$σ$ significance and place upper limits on the molecular gas reservoirs of the other 5, finding molecular gas mass fractions M$_{\rm{H_{2}}}$/M$_{\rm{*}}$=f$_{\rm{H_{2}}}<2-6$% (3$σ$ upper limits). This is 1-2 orders of magnitude lower than coeval star-forming galaxies at similar stellar mass, and comparable to galaxies at $z=0$ with similarly low sSFR. This indicates that their molecular gas reservoirs were rapidly and efficiently used up or destroyed, and that gas fractions are uniformly low ($<$6%) despite the structural diversity of our sample. The implied rapid depletion time of molecular gas (t$_{\rm{dep}}<0.6$ Gyr) disagrees with extrapolations of empirical scaling relations to low sSFR. We find that our low gas fractions are instead in agreement with predictions from both the recent SIMBA cosmological simulation, and from analytical "bathtub" models for gas accretion onto galaxies in massive dark matter halos (log$_{10}M_{\rm{halo}}/\rm{M}_\odot\sim14$ at $z=0$). Such high mass halos reach a critical mass of log$_{10}M_{\rm{halo}}/\rm{M}_\odot>12$ by $z\sim4$ that halt the accretion of baryons early in the Universe. Our data is consistent with a simple picture where galaxies truncate accretion and then consume the existing gas at or faster than typical main sequence rates. Alternatively, we cannot rule out that these galaxies reside in lower mass halos, and low gas fractions may instead reflect either stronger feedback, or more efficient gas consumption.