  A comprehensive study of doped RVB states is performed. It reveals a
fundamental connection between superconductivity and quantum spin fluctuations
in underdoped cuprates :
  {\em Cooper pair hopping} strongly reduces the local magnetization $m_0$.
This effect pertains to recent muon spin rotation measurements in which $m_0$
varies weakly with hole doping in the poorly conducting regime, but drops
precipitously above the onset of superconductivity. Gutzwiller mean field
Approximation (GA) is found to agree with numerical Monte Carlo calculation. GA
shows for example that for a bond amplitude $u(r)=e^{-r/\xi}$, spin spin
correlations decay exponentially with a correlation length $\propto e^{3\pi
\xi^2/2}$. Expectation value of the Heisenberg model is found to be correlated
with average loop density.
