  We study a system of two nanomechanical resonators embedded in a dc SQUID. We
show that the inductively-coupled resonators can be treated as two entangled
quantum memory elements with states that can be read from, or written on by
employing the SQUID as a displacement detector or switching additional external
magnetic fields, respectively. We present a scheme to squeeze the even modeof
the state of the resonators and consequently reduce the noise in the
measurement of the magnetic flux threading the SQUID. Wefinally analyze the
effect of dissipation on the squeezing using the quantum master equation, and
show the qualitatively differentbehavior for the weak and strong damping
regimes. Our predictions can be tested using current experimental capabilities.
