  Recent studies have proposed that the nuclear millimeter continuum emission
observed in nearby active galactic nuclei (AGN) could be created by the same
population of electrons that gives rise to the X-ray emission that is
ubiquitously observed in accreting black holes. We present the results of a
dedicated high spatial resolution ($\sim$60-100 milliarcsecond) ALMA campaign
on a volume-limited ($<50$ Mpc) sample of 26 hard X-ray ($>10$ keV) selected
radio-quiet AGN. We find an extremely high detection rate (25/26 or
$94^{+3}_{-6}\%$), which shows that nuclear emission at mm-wavelengths is
nearly ubiquitous in accreting SMBHs. Our high-resolution observations show a
tight correlation between the nuclear (1-23 pc) 100GHz and the intrinsic X-ray
emission (1$\sigma$ scatter of $0.22$ dex). The ratio between the 100GHz
continuum and the X-ray emission does not show any correlation with column
density, black hole mass, Eddington ratio or star formation rate, which
suggests that the 100GHz emission can be used as a proxy of SMBH accretion over
a very broad range of these parameters. The strong correlation between 100GHz
and X-ray emission in radio-quiet AGN could be used to estimate the column
density based on the ratio between the observed 2-10keV ($F^{\rm
obs}_{2-10\rm\,keV}$) and 100GHz ($F_{100\rm\,GHz}$) fluxes. Specifically, a
ratio $\log (F^{\rm obs}_{2-10\rm\,keV}/F_{100\rm\,GHz})\leq 3.5$ strongly
suggests that a source is heavily obscured [$\log (N_{\rm H}/\rm
cm^{-2})\gtrsim 23.8$]. Our work shows the potential of ALMA continuum
observations to detect heavily obscured AGN (up to an optical depth of one at
100GHz, i.e. $N_{\rm H}\simeq 10^{27}\rm\,cm^{-2}$), and to identify binary
SMBHs with separations $<100$ pc, which cannot be probed by current X-ray
facilities.
