  We have studied the ground state structure of quantum strips within the local
spin-density approximation, for a range of electronic densities between $\sim$
5$\times10^4$ and 2$\times10^6$ cm$^{-1}$ and several strengths of the lateral
confining potential. The results have been used to address the conductance $G$
of quantum strips. At low density, when only one subband is occupied, the
system is fully polarized and $G$ takes a value which is close to
0.7(2e$^2/h$), decreasing with increasing electron density in agreement with
experiments. At higher densities the system becomes paramagnetic and $G$ takes
a value near (2e$^2/h$), showing a similar decreasing behaviour with increasing
electron density. In both cases, the physical parameter that determines the
value of the conductance is the ratio $K/K_0$ of the compressibility of the
system over the free one.
